CN108268688A - A kind of character disc optimum design method based on character shadow beam photoetching technique - Google Patents
A kind of character disc optimum design method based on character shadow beam photoetching technique Download PDFInfo
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- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/39—Circuit design at the physical level
Abstract
Electron beam lithography field in being designed the invention belongs to ic manufacturability, more particularly in the electron beam lithography of character projection, the property that can be overlapped using photoetching inter-character space, by optimization be placed on character disc glazing carve characters symbol position and quantity, the final total exposure number reduced needed for chip manufacturing promotes the throughput of electron beam lithography.The key of the present invention is to propose that one considers character blank overlapping area and the overall target f/A of character frequency of usage/complexity；And propose a kind of method of accurate and effective estimation character real estate；By changing 2 D bin packing algorithms, the final optimization design for realizing character disc.The experimental results showed that method proposed by the present invention is substantially better than current best method known in the world.
Description
Technical field
Electron beam lithography field in being designed the invention belongs to ic manufacturability, and in particular to for a kind of band
The electron beam lithography of character disc (Stencil) and photoetching character (Character), can using the white space of photoetching character
Overlapping property is placed on position and the quantity of the photoetching character on character disc by optimizing, final to reduce needed for chip manufacturing
Total exposure (Shooting) number, so as to promote the method for the throughput of electron beam lithography (throughput).
Background technology
Data is shown, is constantly declined with the characteristic size of Nanometer integrated circuit manufacturing process, in 10 nanometers/7 nanometers rulers
Degree is hereinafter, conventional lithographic techniques face a severe challenge.Several new photoetching processes and technology, such as dual/tri/quadruple/multiple
Lithography layout exposure (Douple/Triple/Multiple Patterning Lithography, DPL/TPL/MPL), extremely purple
Outer Lithography (Extreme Ultra-Violet, EUV), electron beam lithography (Electron Beam Lithography, EBL)
Etc. being suggested and furtherd investigate, above-mentioned technology by as the important candidate technologies below following 10 nanometer technology nodes it
One.
Although DPL/TPL has been widely used in the industrial production of 22 nanometers/14 nanometer technology nodes [1], as spy
Sign size is reduced to 10 nanometers hereinafter, being continuously increased with mask plate (Mask) quantity, mask plate expense in multiple exposure techniques
It drastically increases, while more harsh requirement also proposed to mask plate alignment in manufacturing process.EUV technologies are despite the use of
" Soft X-rays " can reach the wave-length coverage of 10-30nm, improve lithographic accuracy, but at present there are still photoetching underpower,
The technical barrier [2] of mask defects (mask defects) and resistive material (resist materials) etc., causes
The maturity needed for commercial Application has not yet been reached in EUV technologies at present.EBL is the photoetching that one kind does not need to mask plate (massless)
Technology, it can use chip design in the direct photoetching of electron beam to wafer (wafer) under 10 nanometers of size.EBL skills
Art has been applied to the manufacturing of mask plate.Although EBL is one of important candidate of less than 10 nanometers photoetching techniques, it
Presently, there are critical bottleneck problem be that throughput is relatively low, the requirement of chip production factory can not be met.
Most common EBL technologies are variable shaped light beam (Variable Shaped Beam, VSB) technologies, it passes through electronics
One rectangular patterns is directly disposably carved on silicon chip by beam focusing.Such as a H figure shown in Fig. 1 (a), it will be decomposed
For 3 rectangles, as shown in Fig. 1 (b), and VSB photoetching three times is carried out respectively, therefore photoetching efficiency is very low.In order to improve EBL photoetching
Efficiency has developed a kind of character projection (Character Project, CP) technology in the world in recent years.The technology first will figure
Shape is packaged into a pattern, such as pattern H can be synthesized into an entirety, a so-called character is made as, such as Fig. 1 (c) institutes
Show.In CP photoetching, if having some character in chip layout just, it can adjust electron beam and pass through a rectangular opening, become one
Stock cross section for rectangle electron beam and be radiated on the designated character on character disc, so as to by the character photoetching to silicon chip,
As shown in Fig. 1 (d).For the chip layout pattern that can not be found in the character of character disc, then using traditional VSB technologies by
A rectangle carries out photoetching.The technology can significantly promote the efficiency of electron beam lithography.Obviously, character can be found in chip layout
The figure that the frequency of character is higher in disk, is included in character is more complicated (rectangle included is more), and CP photoetching improved efficiencies are brighter
It is aobvious.
In actual production, since the size of character disc is limited, only partial character is selected and is placed into character
In disk, therefore it is the key that improve CP photoetching efficiency to choose the rational position that suitable character is put into character disc.Due to character
There are certain white spaces between square boundary and pattern actual boundary, and as shown in Fig. 1 (c), when placing character, these are empty
It can mutually overlap in vain.In order to place character as much as possible in character disc, the optimal design Problem for solving character disc is defined
For the character disc optimization problem (Overlapping-aware Stencil Planning, OSP) overlapped based on character blank.
In recent years, has numerous studies work in the world for OSP Solve problems.In general, OSP problems can be divided into
1D-OSP and 2D-OSP problems, but they are NP- difficulties problem [3,4].For 1D-OSP, upper and lower blank is big in each character
Small equal, it is commonly used in standard cell design.Document [5,6,7,8] proposes serial of methods and is asked to solve 1D-OSP
Topic, Literature [7] propose a kind of polynomial time optimization algorithm to solve the optimal sequencing of each line character in 1D-OSP
Problem.
For 2D-OSP, the blank of each character upper and lower, left and right four direction can be different.Therefore, it is a kind of aobvious and easy
The character disc mentality of designing seen is that the blank of intercharacter is made full use of to overlap, and character as much as possible is put on character disc.This
Kind algorithm is very similar to " Russia Bricks Game ", that is, selects rational arrangement method, small rectangle as much as possible is put into
In one big rectangle.Document [3] portrays relative position of the character in character disc using ordered pair (Sequence Pair),
Then optimization is designed character disc using simulated annealing, but method does not consider answering comprising pattern in character in [3]
Polygamy causes this method final optimization pass effect limited [9].
Document [4] has used a set of Optimizing Flow effectively to increase the quantity that can be placed in character on character disc.In order to
The white space in character is made full use of, 4 similar characters of blank parts in candidate characters are spliced into one by this method first
A big character；Then the big character comprising 4 characters is reasonably put into character using 2-D bin packing algorithms (bin-packing)
Disk.In order to select the character of pattern complexity as far as possible, [4] first sort all characters by pattern complexity from big to small, selection
The high conduct candidate characters of preceding n complexity.Finally how many a characters can be placed due to not knowing, it is therefore desirable to iteration adjustment n,
Until can not finally be put into.But there are two defects for method in document [4]：(1) big character is connected in by 4 characters are pre-splicing,
May result in big character can not effectively be put into character disc, so as to generate more invalids；2) this method is only for figure
Case complexity is ranked up, more coarse in processing.
For the deficiency in art methods, the present invention intends proposing a kind of efficient character disc optimum design method, especially
It is a kind of character disc optimum design method based on character shadow beam photoetching technique, and chip can be greatly reduced in this method
Exposure frequency during photoetching.
The prior art related to the present invention has：
[1]D.Z.Pan,J s.Yang,K.Yuan,M.Cho,and Y.Ban.Layout optimizations for
double patterning lithography.In ASIC,pages 726–729,2009.
[2]S.Wurm.Transition to euv lithography.In VLSI-TSA,pages 1–2,2012.
[3]B.Yu,K.Yuan,J.-R.Gao,and D.Z.Pan.E-blow:E-beam lithography
overlapping aware stencil planning for mcc system.In DAC,pages 1–7,2013.
[4]J.Kuang and E.F.Y.Young.Overlapping-aware throughput-driven
stencil planning for e-beam lithography.In ICCAD,pages 254–261,2014.
[5]W.-K.Mak and C.Chu.E-beam lithography character and stencil co-
optimization.TCAD,33(5):741–751,2014.
[6]C.Chu and W.-K.Mak.Flexible packed stencil design with multiple
shaping apertures for e-beam lithography.In ASP-DAC,pages 137–142,2014.
[7]D.Guo,Y.Du,and M.D.F.Wong.Polynomial time optimal algorithm for
stencil row planning in e-beam lithography.In ASP-DAC,pages 658–664,2015.
[8]J.Kuang and E.F.Y.Young.A highly-efficient row-structure stencil
planning approach for e-beam lithography with overlapped characters.In ISPD,
pages 109–116.ACM,2014.
[9]Jiabei Ge,Changhao Yan,Hai Zhou,Dian Zhou,Xuan Zeng.An Efficient
Algorithm for Stencil Planning and Optimization in E-Beam Lithography.ASP-
DAC,2017(accepted).。
Invention content
The deficiency that it is an object of the invention to be directed in art methods provides a kind of efficient character disc optimization design
Method, especially a kind of character disc optimum design method based on character shadow beam photoetching technique, this method can be significantly
Reduce exposure frequency during chip photoetching.
In the method for the present invention：(1) it proposes one and considers character blank and overlap and character frequency of usage/complexity
Index f/A, the general emphasis of traditional algorithm consider how the white space of character fully overlaps this " geometric area characteristic
(Area) " it on, and is directed on the frequency of usage of each character and " frequency characteristic (frequency) " of character complexity itself and examines
Consider less；The present invention proposes that the frequency divided by character using character are put into rear shared area, i.e. can f/A be chosen as character
The key index entered, conceptually, those highest characters of character disc unit area utilization ratio should be selected into；(2) in character
And its before periphery character is not put into completely, it is more difficult for how accurately estimating the real estate of character, and the present invention carries
A kind of accurate and effective character area occupied evaluation method is gone out；(3) f/A indexs set forth above and area reckoning side are utilized
Method, by changing 2-D bin packing algorithms, the final optimization design for realizing character disc.
Specifically, the present invention is based on character projection lithography technologies, it is proposed that a kind of efficient character disc optimum design method,
This method includes key step：First, the position candidate for preparing to be put into character is determined based on 2-D bin packing algorithms；Secondly, according to time
Bit selecting is put and its boundary areas case, estimates the possibility area occupied of each candidate characters；Then, for each candidate word
Symbol calculates and has considered character blank and overlap index f/A with character frequency of usage/complexity；Finally, from candidate characters
The character for choosing f/A index maximums is put into character disc；Above step is repeated, is until any character can not be put into character disc
Only.Exposure frequency during chip photoetching can be greatly reduced in the method for the present invention, and flow is as shown in Figure 2.
More specifically, a kind of efficient character disc optimum design method based on character projection lithography technology of the invention；Its
It is characterized in, considers character blank overlapping area and the overall target f/A of character frequency of usage/complexity, and utilize using one
A kind of method of accurate estimation character real estate realizes the optimization design of character disc by changing 2-D bin packing algorithms,
Including：
Input parameter：
1st, an empty character disc, height H, width W；
2nd, character set, wherein include the geological information of each character, i.e. height h, width w, upper and lower, left and right gutter
It is respectively t, b, l, r to divide width；The frequency number T that character occurs in chip layout；The rectangle number vsb included in character；
Export result：
The character set and the position coordinates of each character being put into character disc.
The design method of the present invention, including step：
Step 1：Skyline is established based on 2-D bin packing algorithms to preserve the current occupied state of character disc, and from
The minimum line segment of a height is chosen in Skyline as the position candidate to be placed into character, then from character set to be filled
In filter out candidate characters collection；
Step 2：Judge whether flow terminates.If the candidate characters that step 1 obtains integrate not as empty set, step 3 is gone to；If
Candidate characters collection is sky, then attempts to update Skyline；If being successfully updated Skyline, 1 is gone to step；It otherwise, can not be further
It fills character, flow terminates；
Step 3:According to the position candidate that step 1 obtains, the synthesis that candidate characters concentrate each candidate characters is calculated one by one
Index f/A；
Step 4：The character for choosing overall target f/A maximums is concentrated from candidate characters, and deletes and is somebody's turn to do from input character set
Then it in a manner that lower left is aligned is put into character disc, and record the character and the position being put into, updates by character
Skyline is turning lastly to step 1.
In step 1 of the present invention, the core data of two-dimentional bin packing algorithm is Skyline, and Skyline is defined as horizontal line section
Set, these horizontal line sections are made of the top line segment for being put into character, and only retain the y directions highest part of height, i.e., to appointing
One x coordinate of meaning only retains the line segment aggregate that the highest point of y values is formed, as shown in Fig. 3 (b), for any one in Skyline
Line segment includes starting X-coordinate xa, terminates X-coordinate xb, line width a, Y-axis coordinate y, left side space width SL, right side blank
The information such as width S R and underlying empty width S B；
There is following four operation to the line segment in Skyline：
(1) lifting operation, function are the height for specifying the lifting of certain line segment；It is a kind of it is special flush lifting operation be by
Line segment is raised to be flushed with that line segment relatively low in the adjacent segments of left and right；As shown in figure 4, intend lifting line segment 2, due to line segment 2
In the line segment 1 and line segment 3 of the left and right sides, line segment 1 is relatively low, therefore is lifted line segment 2 and is flushed to line segment 1, i.e. dotted line position in Fig. 4
It puts；The height y of line segment 2 is updated simultaneously2With underlying empty width S B2For：
y2=min (y1,y3) (1)
Wherein y1、y3The respectively height y values of line segment 1 and line segment 3, SB1、SB3The respectively sky of 3 lower section of line segment 1 and line segment
Bai Kuandu；The other information of line segment 2 remains unchanged；
(2) union operation if the identical and left and right of two lines section height is adjacent, can be merged into a new line segment；Such as
Shown in Fig. 4, after line segment 2 is lifted, a line segment can be merged into line segment 1；Specifically union operation is：From existing Skyline
It is middle to delete two lines section to be combined, and a new line segment is generated, the information which includes is：Y=y1；Xa=xa1；xb
=xb2；A=a1+a2；SL=SL1；SB=min (SB1, SB2)；SR=SR2, the wherein parameter of subscript 1 and subscript 2 is respectively to close
And front left side line section 1 and the parameter of right side line segment 2；
(3) line segment is split into two lines section by splitting operation at some intermediate point；Specific splitting operation
To delete a line segment to be divided from existing Skyline, and generate 2 new line segments；Specially：
y1=y；xa1=xa；xb1=xa+al；a1=al；SB1=SB；SL1=SL；SR1=S0
y2=y；xa2=xa+al；xb2=xb；a2=a-al；SB2=SB；SL2=S0；SR2=SR
Wherein the parameter of subscripting 1,2 is respectively the left side and right side bearing segment information after dividing；Before no subscript parameters is divisions
Line segment information；Al is left side line segment length at split point；S0For gap width at split point；
(4) update operation after a character is placed in a manner that lower-left is aligned on certain line segments in Skyline, needs
Will line segment where more fresh character information；As shown in figure 5, Fig. 5 (a) representatives are put into the state of skyline before character, Fig. 5 (b) generations
Table is put into the state of skyline after character；Concrete operations are：
1) left side line segment 1 is divided along the left frame boundary of character, and the right part after line segment 1 is divided is raised to character
Upper edge at, as shown in Fig. 5 (b) Green line segments；
2) along the left frame boundary of character division right-hand line section 2, the left part after line segment 2 is divided is raised to character
At upper edge, as shown in line segment red in Fig. 5 (b)；
3) 1 right half of line segment and 2 left half of line segment are merged into new line segment 3.
Step 1 of the present invention specifically comprises the following steps：
Step 1.1：Choose Skyline in height y minimum line segment (during initialization Skyline for only include a y=0,
Width is the horizontal line section of W)；If there is a plurality of line segment height y identical, the line segment of the leftmost side (i.e. xa is minimum) is taken as candidate bit
It puts, as shown in Figure 6；
Step 1.2：All characters for being put into position candidate are chosen from character set and add in candidate characters collection.In lower left side
In the case of alignment, the character that can be put into must meet interval S1>=0 and S2>=0, as shown in fig. 7, S1And S2For：
The parameter that wherein parameter l, r, w is character size information and xa, xb, SL, SR are corresponding line segment in Skyline；
When the character that can be put into position candidate is not present in character set, candidate characters collection is set to empty set.
In step 2 of the present invention, judge whether flow terminates；If the candidate characters that step 1 obtains integrate as nonempty set, turn
Step 3, whether otherwise judge the line segment of position candidate in Skyline can be lifted and union operation；If it can be lifted and close
And be then lifted and merge, 1.1 are then gone to step, otherwise, can not further be filled character, is exported as a result, flow terminates.
In step 3 of the present invention, for each character that candidate characters are concentrated, overall target f/A is calculated, wherein f is represented
The frequency/complexity characteristics of character, A represent the area that actual capabilities occupy when character is put into character disc；It includes sub-step：
Step 3.1：The present invention calculates the frequency/complexity characteristics f of each character according to formula (4)：
F=T (vsb-1) (4)
The characterization in this character is selected into character disc, diminishbb exposure frequency；
Accurately to estimate the occupied area A of character, character top, left side, right side, internal occupancy face are directed in the present invention
Integration is not estimated that the difference according to position candidate has different evaluation methods, is as follows：
Step 3.2：For the area occupied above character, there are following three kinds of different estimations for the difference of position candidate
Method, as shown in figure 8, wherein the character of grey is the character of area occupied to be calculated, top and the blank above character disc
Interval St, can be divided into successively according to size：Other characters can not be put into, 1 other character can be put into, at least two can be put into
Other three kinds of situations of character, respectively as shown in Fig. 8 (a), Fig. 8 (b) and Fig. 8 (c), then area occupied A above this characterTEstimation
For：
(1) if top interval StIt is too small, when can not be put into any one other character C ', ATFor blank face above this character C
Product (red area in Fig. 8 (a))+top waste area (Fig. 8 (a) Greens region)；
(2) if can only be put into an other character C ', ATFor (the red color area in Fig. 8 (b) of blank area above this character
Domain)；
(3) during other situations, ATFor the half of blank area above this character, i.e. the one of red area area in Fig. 8 (c)
Half；
Described, area occupied A above this characterTIt is provided by formula (5)：
Wherein w, h, l, r, t, b are the correspondingly-sizeds of this character C, and parameter h ', t ', b ' and parameter b " are candidate characters respectively
The correspondingly-sized of other character C ' and C " are concentrated, wherein top interval StBy formula (6)：
St=H- (y-min (SB, b)+h) (6)
Wherein, H is the height of character disc, and y is the Y coordinate of place line segment；
Step 3.3：For the area occupied on the character left side, for position candidate different, there are two types of different estimation sides
Method；As shown in figure 9, wherein the character of grey is the character of area occupied to be calculated, the left side is with having character on character disc
Blank spacing can be divided into successively according to size：Any one other character can not be put into, at least one other character two can be put into
Kind situation, such as Fig. 9 (a), Fig. 9 (b) are shown respectively, then this character left side area occupied ALIt is estimated as：
(1) if the left side can not be put into any other character, i.e. interval S3<0 or S4<When 0, ALFor this character left margin face
Product (red area in Fig. 9 (a))+left side waste area (Fig. 9 (a) Greens region)；
(2) during other situations, ALFor the half of this character left margin area, i.e. the one of red area area in Fig. 9 (b)
Half；
Described, this character left side area occupied ALIt is provided by formula (7)：
Wherein ml=(y "-SB ")-(y '-SB '), nl=(xb '-min (SL, l))-(xa '-SL ') is this character left side wave
Take the length of side of area, pl=(y-min (SB, b)+h)-(y '-SB ') is the height of left margin, S3And S4(Fig. 9 (b) shown in) by
Formula (8) provides：
Wherein without ', band ' and band " parameter be line segment L and character C, line segment L ' and character C ', line segment L respectively "
Relevant parameter；
Step 3.4：For the area occupied A on the right of characterR, it is similar with step 3.3, have two for the difference of position candidate
The different evaluation method (shown in Figure 10) of kind, i.e., area occupied A on the right of this characterRIt is provided by formula (9)：
Wherein mr=y '-(y-SB), nr=(xb+SR)-(xa-min (SL, l)+w) is the side of waste area on the right of this character
It is long, pr=(y-min (SB, b)+h)-(y-SB) be the right blank height, S5And S6It is provided by formula (10)：
Parameter wherein without ', band ' is the relevant parameter of line segment L and character C, line segment L ' and character C ' respectively；
Step 3.5：Total area occupied A is obtained by formula (11)：
A=AT+AL+AR+AI (11)
Wherein AT、AL、ARIt is the area occupied on upper, left and right side respectively；AIIt is character inner real estate, such as Figure 11
Shown red area area is provided by formula (12)：
AI=lh1+(w-l-r)·h2 (12)
Wherein h1=(y '-SB ')-(y-SB) and h2=(y-min (SB, b)+h-t)-(y-SB) is corresponding height in figure,
Parameter wherein without ', band ' is line segment L and character C respectively, the relevant parameter of line segment L '；
Step 3.6：Calculate the overall target f/A that candidate characters concentrate character, the i.e. frequency/complexity f divided by area occupied
A。
After character disc design solves, all character sets and its specific coordinate position in character disc are can obtain, because
This, under the character disc design result obtained in the present invention, chip exposure frequency S# is obtained by formula (13)：
Wherein SCRepresent the character set of input, SC1Represent the character set being put on character disc, CiFor i-th of character.
The advantage of the invention is that：
The geometric area of character and frequency characteristic in 2D-OSP are solved the problems, such as 1. having considered, and are proposed a kind of effective comprehensive
The method for closing index f/A and quick estimation character area occupied；
2. the present invention do not need to character carry out it is pre-splicing, without the character number to can finally be placed in character disc into
Row is estimated and iteration, realizes simple.
3. existing example show the present invention no matter character quantity in character disc is put into or final exposure frequency,
Significantly substantially EBL efficiency is improved better than current best method known in the world.
Description of the drawings
Fig. 1 is the model schematic of character shadow casting technique.
Fig. 2 is the flow chart of the method for the present invention.
Fig. 3 is the dimension information schematic diagram of character size information and Skyline middle conductors.
Fig. 4 is the schematic diagram to the lifting of Skyline middle conductors and union operation.
Fig. 5 is the schematic diagram that operation is updated to Skyline middle conductors.
Fig. 6 is the schematic diagram for choosing position candidate.
Fig. 7 is that the condition judgment schematic diagram of a character whether can be put into position candidate.
Fig. 8 is the schematic diagram of estimation top area occupied.
Fig. 9 is the schematic diagram for estimating left side area occupied.
Figure 10 is the schematic diagram of estimation the right area occupied.
Figure 11 is the schematic diagram of the internal area occupied of estimation.
Specific embodiment
Now by the implementation process of specific example, to illustrate the advantage of the method for the present invention.
Implement example 1
The character disc size that this example uses is 1000um X 1000um, and character boundary is according to different examples, respectively
38um X 38um, 40um X 40um, 42um X 42um, 44um X 44um, number are 1000, and whole examples come from document
[3]。
Of the invention and international existing method, the i.e. comparison result of document [3] and document [4] are shown in as shown in table 1.It can be with
See, 23% is promoted than the result of document [3] on the number of characters that result of the present invention can be put on character disc, than document [4]
As a result about 6.0% is promoted.On total exposure number, the result than document [3] is reduced by about 2.04 times, and the result than document [4] subtracts
It is about 0.47 times few.
1 character disc size of table is that the example of 1000um X 1000um compares
Implement example 2
The character disc size that this example uses is 2000um X 2000um, and character boundary is according to different examples, respectively
38um X 38um, 40um X 40um, 42um X 42um, 44um X 44um, number are 4000, and whole examples come from document
[3]。
Of the invention and international existing method, the i.e. comparison result of document [3] and document [4] are shown in as shown in table 2.It can be with
See, 30% is promoted than the result of document [3] on the number of characters that result of the present invention can be put on character disc, than document [4]
As a result 13% is promoted.On total exposure number, the result than document [3] is reduced by about 2.62 times, and the result than document [4] is reduced about
1.78 again.
2 character disc size of table is that the example of 2000um X 2000um compares
Above-mentioned example show the present invention no matter character quantity in character disc is put into or final exposure frequency, it is bright
It is aobvious to be substantially better than current best method known in the world, improve EBL efficiency.
Claims (7)
1. a kind of efficient character disc optimum design method based on character projection lithography technology；It is characterized in that using a consideration
The overall target f/A of character blank overlapping area and character frequency of usage/complexity, and it is practical using a kind of accurate estimation character
The method of area occupied realizes the optimization design of character disc by changing 2-D bin packing algorithms, including：
Input parameter：
1st, an empty character disc, height H, width W；
2nd, character set, wherein include the geological information of each character, i.e. height h, width w, upper and lower, left and right blank parts are wide
Degree is respectively t, b, l, r；The frequency number T that character occurs in chip layout；The rectangle number vsb included in character；
Export result：
The character set and the position coordinates of each character being put into character disc；
In the steps below：
Step 1：Skyline is established based on 2-D bin packing algorithms to preserve the current occupied state of character disc, and from Skyline
Then the middle minimum line segment of a height of choosing is filtered out as the position candidate to be placed into character from character set to be filled
Candidate characters collection；
Step 2：Judge whether flow terminates；If the candidate characters that step 1 obtains integrate as empty set, step 3 is gone to；If candidate word
Symbol collection is sky, then attempts to update Skyline；If being successfully updated Skyline, 1 is gone to step；Otherwise, word can not further be filled
Symbol, flow terminate.
Step 3:According to the position candidate that step 1 obtains, the overall target that candidate characters concentrate each candidate characters is calculated one by one
f/A；
Step 4：The character for choosing overall target f/A maximums is concentrated from candidate characters, puts it into character disc and records the word
The position for according with and being put into updates Skyline, then goes to step 1.
2. method as described in claim 1, it is characterized in that, the core data of two-dimentional bin packing algorithm is in the step 1
Skyline；Skyline is defined as the set of horizontal line section, and the horizontal line section is made of, and only the top line segment for being put into character
Retain the y directions highest part of height, i.e., to any one x coordinate, only retain the line segment aggregate that the highest point of y values is formed；It is right
Any one line segment in Skyline comprising starting X-coordinate xa, terminates X-coordinate xb, line width a, Y-axis coordinate y, left side sky
The information such as Bai KuanduS L, right side blank width S R and underlying empty width S B；
There is following four operation to the line segment in Skyline：
(1) lifting operation, function are the height for specifying the lifting of certain line segment；A kind of special lifting operation that flushes is by line segment
It is raised to and is flushed with that line segment relatively low in the adjacent segments of left and right；If intending lifting line segment 2, and assume 2 left and right sides of line segment
In line segment 1 and line segment 3, line segment 1 is relatively low, therefore is lifted line segment 2 and is flushed to line segment 1；The height y of line segment 2 is updated simultaneously2With under
Square space width SB2For：
y2=min (y1,y3) (1)
Wherein y1、y3The respectively height y values of line segment 1 and line segment 3, SB1、SB3The blank of respectively 3 lower section of line segment 1 and line segment is wide
Degree；The other information of line segment 2 remains unchanged；
(2) union operation if the identical and left and right of two lines section height is adjacent, can be merged into a new line segment；Assuming that line
Section 2 can merge into a line segment with line segment 1.Specifically union operation is：To be combined two are deleted from existing Skyline
Line segment, and a new line segment is generated, the information which includes is：Y=y1；Xa=xa1；Xb=xb2；A=a1+a2；SL=
SL1；SB=min (SB1, SB2)；SR=SR2, the wherein parameter of subscript 1 and subscript 2 is respectively to merge front left side line section 1 and right side
The parameter of line segment 2；
(3) line segment is split into two lines section by splitting operation at some intermediate point；Specific splitting operation is, from
A line segment to be divided is deleted in existing Skyline, and generates 2 new line segments；Specially：
y1=y；xa1=xa；xb1=xa+al；a1=al；SB1=SB；SL1=SL；SR1=S0
y2=y；xa2=xa+al；xb2=xb；a2=a-al；SB2=SB；SL2=S0；SR2=SR
Wherein the parameter of subscripting 1,2 is respectively the left side and right side bearing segment information after dividing；No subscript parameters are line segment before division
Information；Al is left side line segment length at split point；S0For gap width at split point；
(4) update operation after a character is placed in a manner that lower-left is aligned on certain line segments in Skyline, needs more
Information where fresh character near line segment；Specifically operate in the steps below：
1) left side line segment 1 is divided along the left frame boundary of character, and the right part after line segment 1 is divided is raised to the upper of character
Edge；
2) along the left frame boundary of character division right-hand line section 2, the left part after line segment 2 is divided is raised to the top of character
At；
3) 1 right half of line segment and 2 left half of line segment are merged into new line segment 3.
3. method as described in claim 1, it is characterized in that, Skyline is established based on 2-D bin packing algorithms in the step 1 and is used
To preserve the current occupied state of character disc, and choose the minimum line segment of a height from Skyline and be used as to be placed into character
Position candidate, candidate characters collection is then filtered out from character set to be filled；Include the following steps：
Step 1.1：(Skyline is only comprising a y=0, width to the line segment of height y minimums during initialization in selection Skyline
Horizontal line section for W)；If there is a plurality of line segment height y identical, the line segment of the leftmost side (i.e. xa is minimum) is taken as position candidate；
Step 1.2：All characters for being put into position candidate are chosen from character set and add in candidate characters collection；It is aligned in lower left side
In the case of, the character that can be put into must meet interval S1>=0 and S2>=0, S1And S2It is defined as by formula (3)：
The parameter that wherein parameter l, r, w is character size information and xa, xb, SL, SR are corresponding line segment in Skyline；
When the character that can be put into position candidate is not present in character set, candidate characters collection is set to empty set.
4. method as described in claim 1, it is characterized in that, judge whether flow terminates in the step 2；If step 1
Whether the candidate characters arrived integrate as nonempty set, then go to step 3, otherwise judge the line segment of position candidate in Skyline and can carry out
Lifting and union operation；If can be lifted and merge, then lifting and merging go to step 1.1, otherwise, can not further fill out
Character is filled, is exported as a result, flow terminates.
5. method as described in claim 1, it is characterized in that, each character concentrated in the step 3 for candidate characters,
Overall target f/A is calculated, wherein f represents the frequency/complexity characteristics of character, and A represents actual capabilities when character is put into character disc
The area of occupancy.
6. method as described in claim 1, it is characterized in that, it is the accurate estimation occupied area A of character in the step 3,
It will respectively be estimated for character top, left side, right side, internal area occupied；According to the different using different of position candidate
Evaluation method, as follows：
Step 3.2：For the area occupied above character, following three kinds of different estimation sides are used for the difference of position candidate
Method；According to the character of area occupied to be calculated, top and the blank interval S above character disct, can divide successively according to size
For：Other characters can not be put into, 1 other character can be put into, at least two three kinds of situations of other characters can be put into；Then this word
Symbol top area occupied ATIt is estimated as：
(1) if top interval StIt is too small, when can not be put into any one other character C ', ATFor blank area above this character C+
Top wastes area；
(2) if can only be put into an other character C ', ATFor blank area above this character；
(3) during other situations, ATHalf for blank area above this character；
Area occupied A above this described characterTIt is provided by formula (4)：
Wherein w, h, l, r, t, b are the correspondingly-sizeds of this character C, and parameter h ', t ', b ' and parameter b " are that candidate characters are concentrated respectively
The correspondingly-sized of other character C ' and C ", wherein top interval StBy formula (5)：
St=H- (y-min (SB, b)+h) (5)
Wherein, H is the height of character disc, and y is the Y coordinate of place line segment；
Step 3.3：For the area occupied on the character left side, for position candidate different, there are two types of different evaluation methods；It treats
The character of area occupied, the left side and the blank spacing for having character on character disc are calculated, can be divided into successively according to size：It can not
It is put into any one other character, at least one other two kinds of situations of character can be put into；Then this character left side area occupied ALEstimate
It is：
(1) if the left side can not be put into any other character, i.e. interval S3<0 or S4<When 0, ALFor this character left margin area+left side
Side wastes area；
(2) during other situations, ALHalf for this character left margin area；
This character left side area occupied ALIt is provided by formula (6)：
Wherein ml=(y "-SB ")-(y'-SB'), nl=(xb'-min (SL, l))-(xa'-SL') is this character left side waste face
The long-pending length of side, pl=(y-min (SB, b)+h)-(y'-SB') is the height of left margin, S3And S4It is provided by formula (7)：
Wherein without the corresponding of ', band ' and band " parameter be line segment L and character C, line segment L ' and character C ', line segment L respectively "
Parameter；
Step 3.4：For the area occupied A on the right of characterR, similar with step 3.3, for position candidate different, there are two types of not
Area occupied A on the right of same evaluation method, i.e. this characterRIt is provided by formula (8)：
Wherein mr=y'- (y-SB), nr=(xb+SR)-(xa-min (SL, l)+w) is the length of side of waste area on the right of this character,
pr=(y-min (SB, b)+h)-(y-SB) be the right blank height, S5And S6It is provided by formula (9)：
Parameter wherein without ', band ' is the relevant parameter of line segment L and character C, line segment L ' and character C ' respectively；
Step 3.5：Total area occupied A is obtained by formula (10)：
A=AT+AL+AR+AI (10)
Wherein AT、AL、ARIt is the area occupied on upper, left and right side respectively；AICharacter inner real estate by formula (11) to
Go out：
AI=lh1+(w-l-r)·h2 (11)
Wherein h1=(y'-SB')-(y-SB) and h2=(y-min (SB, b)+h-t)-(y-SB) is corresponding height in figure, wherein
Parameter without ', band ' is line segment L and character C respectively, the relevant parameter of line segment L '.
7. method as described in claim 1, it is characterized in that, it is concentrated in the step 4 from candidate characters and chooses overall target f/A
The character of numerical value maximum, and the character is deleted from input character set, it is then put into character in a manner that lower left is aligned
In disk, and the character and the position being put into are recorded, update Skyline.
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| CN112232587A (en) * | 2020-10-29 | 2021-01-15 | 华东计算技术研究所（中国电子科技集团公司第三十二研究所） | Combined optimization method and system based on improved Skyline algorithm |
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| CN112232587B (en) * | 2020-10-29 | 2023-08-11 | 华东计算技术研究所（中国电子科技集团公司第三十二研究所） | Combination optimization method and system based on improved Skyline algorithm |
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