CN104462628A - Construction method and device for barrier-bypassing eight-fork Steiner minimum tree - Google Patents
Construction method and device for barrier-bypassing eight-fork Steiner minimum tree Download PDFInfo
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- CN104462628A CN104462628A CN201310439047.3A CN201310439047A CN104462628A CN 104462628 A CN104462628 A CN 104462628A CN 201310439047 A CN201310439047 A CN 201310439047A CN 104462628 A CN104462628 A CN 104462628A
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Abstract
The invention belongs to the technical field of integrated circuits and particularly relates to a construction method and device for a barrier-bypassing eight-fork Steiner minimum tree used for automatic wire arrangement of an X-shaped interconnection structure. According to the method, firstly, an Escape graph and a grid matrix of a wire arrangement plane are obtained; secondly, a barrier-bypassing right-angle Steiner minimum tree is obtained through the graph decomposition technology, the Steiner tree construction technology and the combination technology; thirdly, five kinds of geometric transformation are introduced according to newly-added 45-degree and 135-degree wire arrangement trends, and finally the required barrier-bypassing eight-fork Steiner minimum tree is obtained. The device comprises an input unit, an output unit, a program storage unit, an external bus, a memory, a storage management unit, an input and output bridging unit, a system bus and a processor. A program for the construction method of the Steiner minimum tree is stored in the program storage unit. By means of the construction method and device, a wire arrangement result of the barrier-bypassing eight-fork Steiner minimum tree of an input line network can be obtained quickly and effectively.
Description
Technical field
The invention belongs to integrated circuit fields, relate to a kind of construction method of eight fork Steiner minimum tree of cut-through thing.Be specifically related to a kind of eight fork Steiner minimum tree construction method and devices thereof of the cut-through thing for X-type interconnection structure automatic wiring.
Background technology
Steiner minimum tree problem is a classical problem in Combinatorial Optimization, computational geometry, has important application in fields such as computer network layout, circuit design, bio-networks analyses.Traditional Steiner minimum tree and various variation thereof, be subject to the extensive concern of Chinese scholars for many years always.Due to the vital role in integrated circuit wiring, the right angle Steiner minimum tree building cut-through thing has become a large focus of this area Recent study.
On the other hand, along with novel interconnection structure as the X of IC chip interconnect (X-Architecture), the rise of the self routing of network-on-chip (NOC) and PCB, 45 degree of eight fork wiring of on-right angle causes the pay attention to day by day of academia and industry member because it reduces the potentiality of line length.Have the experimental result of research to show compared to right angle wiring, eight fork wirings can reduce total line length of nearly 20% and the via count of 30%, are conducive to obtaining and design more efficiently.
Because eight fork Steiner minimum tree problems belong to NP-Hard, the heuritic approach that energy rapid build eight pitches Steiner minimum tree is mainly found in current research.But about the situation of barrier in practical wiring is not still considered in research.Although there is research to consider obstacle, building process needs the division carrying out generation figure, implements very complicated, considers the long not necessarily optimum of Steiner tree line that temporal constraint obtains simultaneously.In order to solve now methodical deficiency, present inventor intends proposing a kind of method and apparatus fast and effeciently building eight fork Steiner minimum tree of cut-through thing.
Prior art related to the present invention has following list of references:
[1]E.N.Gilbert and H.O.Pollak.Steiner minimal trees.SIAM J.Appl.Math.,16(1):1–29,1968
[2]Chih-Hung Liu,Sy-Yen Kuo,Lee,D.T,et al.Obstacle-Avoiding RectilinearSteiner Tree Construction:A Steiner-Point-Based Algorithm[J].IEEETransactions on Computer-Aided Design of Integrated Circuits and Systems,2012,31(7):1050-1060.
[3]Gaurav Ajwani,Chris Chu and Wai-Kei Mak.FOARS:FLUTE BasedObstacle-Avoiding Rectilinear Steiner Tree Construction[J].IEEE Transactionson Computer-Aided Design of Integrated Circuits and Systems,2011,30(2):194-204.
[4]Yen-Hung Lin,Shu-Hsin Chang,Yih-Lang Li.Critical-Trunk-BasedObstacle-Avoiding Rectilinear Steiner Tree Routings and Buffer Insertion forDelay and Slack Optimization[J].IEEE Transactions on Computer-Aided Designof Integrated Circuits and Systems,2011,30(9):1335-1348.
[5]S.P.Shang,X.D.Hu and Tong Jing.Average Lengths of Wire Routing underM-Architecture and X-Architecture[C]//Proceeding of International Symposiumon Circuits and Systems(ISCAS),2006:321-324.
[6]Chia-Chun Tsai,Ghung-Chieh Kuo,et al.X-architecture Clock TreeConstruction Associated with Buffer Insertion and Sizing[M].Asia Symposium onQuality Electronic Design,2009:298-303.
[7]Chifeng Wang,Wen-Hsiang Hu,et al.Scalable load balancing congestion-awareNetwork-on-Chip router architecture[J].Journal of Computer and System Sciences,2013,79(4):421-439.
[8]Kyosuke Shinoda,Yukihide Kohira,et al.Single-Layer Trunk Routing UsingMinimal45-Degree Lines[J].IEICE Transactions on Fundamental of Electronics,Communication and Computer Science,2011,94(12):2510-2518.
[9]S.Teig,The X Architecture:not your father’s diagonalwiring[C]//Proceeding of ACM System Level Interconnect Prediction,2002:33–37.
[10]Matthias Müller-Hannemann,Anna Schulze.Hardness and Approximation ofOctilinear Steiner Trees[C]//Proceedings of the16
thInternational Symposium onAlgorithms and Computation,2005:256-265.
[11]Charles Chiang,Ching-Shoei Chiang.Octilinear Steiner treeconstruction[C]//Proceedings of the45th Midwest Symposium on Circuits andSystems,2002:603-606.
[12]Qi Zhu,Hai Zhou,et al.Efficient octilinear steiner tree constructionbased on spanning graphs[C]//Proceedings of Asia and South Pacific DesignAutomation Conference(ASP-DAC),2004:687-690.
[13]ChenFeng Chang,Yao-Wen Chang.X-Route:An X-architecture full-chipmultilevel router[C]//Proceedings of IEEE International SOC Conference,2007:229-232.
[14]Hsin-Hsiung Huang,Chung Yuan,et al.Timing-driven X-architecture routeramong rectangular obstacles[C]//Proceedings of IEEE International Symposiumon Circuits and Systems,2008:1804-1807.
[15]VoB S.Steiner’s problem in graphs:heuristic methods[J].Discrete AppliedMathematics,1992,40(1):45-72.
Summary of the invention
The object of the invention is to overcome the deficiencies in the prior art, propose a kind of method and apparatus fast and effeciently building eight fork Steiner minimum tree of cut-through thing.Especially for novel X interconnect architecture, a kind of automatic wiring method and apparatus of the eight fork Steiner minimum tree based on structure cut-through thing is provided.
The method and apparatus that the present invention proposes specifically describes as follows:
The individual end points V={V to be connected of given n on routing planes
1, V
2..., V
nand m rectangular obstruction O={O
1, O
2..., O
n, it is desirable to utilize to build along the eight fork limits in directions and additional insertion Steiner point one connect all end points V, not by any barrier O, and the tree that total line length is the shortest, be cut-through thing eight pitch Steiner minimum tree; If it can only be horizontal or vertical for limiting wiring direction, be then the right angle Steiner minimum tree of cut-through thing.
More specifically, the construction method of eight fork Steiner minimum tree of cut-through thing of the present invention, building process as shown in Figure 1, mainly comprises the steps:
Step 1: the rail network structure file of input circuit.
This rail network structure file describes on routing planes, the coordinate position of n end points to be connected and m rectangular obstruction.
Step 2: obtain Escape figure corresponding to this routing planes and grid matrix.
First do level and vertical curve through each end points to be connected and barrier summit, until run into the outer boundary of barrier, the grid chart obtained is called that Escape schemes.If there is N number of x coordinate (x in the summit of end points to be connected and barrier
1, x
2..., x
n), M y coordinate (y
1, y
2..., y
m), set up M × N matrix A, wherein an a
ijrepresent net point (x in plane
j, y
i) type.Wherein, 0 represents that lattice point is arranged in rectangular obstruction, and 1 represents that barrier does not belong to the lattice point that can insert Steiner point outward, Steiner point can be inserted outside 2 expression barriers, 3,4,5,6 represent respectively and are positioned at that four, barrier is borderline inserts Steiner point, 7,8,9,10 four summits representing barrier respectively, 11 represent end points to be connected.Utilize grid matrix, the type of lattice point can be determined in the geometric transformation below fast, and then make corresponding process.
Step 3: utilize the decomposition of figure, the structure of Steiner tree and folding to obtain the right angle Steiner minimum tree of cut-through thing of this gauze wiring.Detailed process is following step by step:
Step by step 31: the trimming collection utilizing Escape figure, is several strongly connected componentses by diagram root, and carries out the simplification of this figure.
According to the trimming collection obtained and strongly connected components collection, original Escape figure can be converted into new figure, the strongly connected components that its vertex representation obtains, its limit represents the trimming obtained.Obviously, the new figure obtained is one tree.If there is no end points to be connected in the strongly connected components of the leaf node representative of this tree, then from original Escape figure, remove this connected component.Repeat this process until eliminate all similar leaf nodes, thus simplify original Escape figure.
Step by step 32: in 31 each strongly connected componentses obtained step by step, build initial Steiner minimum tree.The initial Steiner minimum tree of concrete structure is following step by step:
Step 321: choose on figure and spend two maximum summits as initial tree T
1and T
2.
Step 322: choose in residue summit, distance T
1or T
2nearest summit, joins T along its shortest path
1or T
2on, and upgrade T thus
1and T
2.
Step 323: if it is untreated to there is summit, turn to step 322.Otherwise, utilize T
1and T
2between shortest path connect T
1and T
2, obtain complete Steiner minimum tree.
Step by step 33: in each strongly connected components, carry out the decomposition of subtree and merge and optimize initial Steiner minimum tree further.
For by 32 initial Steiner minimum tree obtained step by step, remove a limit wherein, produce two stalks trees, if the bee-line between them is less than the length of side removed, then utilizes this shortest path to connect and merge this two subtree.Repeat this process, until all limits all process, thus optimize initial Steiner minimum tree further.
Step by step 34: the Steiner minimum tree in all strongly connected componentses using trimming collection to connect to merge above-mentioned steps to obtain, thus obtain the right angle Steiner minimum tree of the cut-through thing of this routing planes.
Step 4: the right angle Steiner minimum tree obtained for step 3, makes full use of newly-increased 45,135 degree of wiring trends, carries out 5 kinds of basic geometric transformations, reduces total line length further.
Geometric transformation 1) as shown in Figure 2, total line length decreases
Geometric transformation 2) as shown in Figure 3, total line length decreases
Geometric transformation 3) as shown in Figure 4, total line length decreases
Geometric transformation 4) as shown in Figure 5, total line length decreases
Geometric transformation 5) as shown in Figure 6, total line length decreases
Step 5: the eight fork Steiner minimum tree obtaining cut-through thing, and carry out global optimization, reduce the line length of wiring further.
The invention provides the device of the eight fork Steiner minimum tree methods based on above-mentioned structure cut-through thing, as shown in Figure 7: comprise input block (102), output unit (103), program storage unit (PSU) (105), external bus (110), internal memory (106), memory management unit (107), input and output bridge-jointing unit (108), system bus (111) and processor (109), wherein, described input block (102), output unit (103) and program storage unit (PSU) (105) are directly connected to described external bus (110), and external bus (110) is connected with described system bus (111) by input and output bridge-jointing unit (108).Described internal memory (106) is connected to system bus (111) by memory management unit (107).Described processor (109) is directly connected to system bus (111).The program module (104) of the method for the eight fork Steiner minimum tree effectively building cut-through thing is fast stored in program storage unit (PSU) (105).
The described program module (104) effectively building the method for eight fork Steiner minimum tree of cut-through thing fast can be realized by programming languages such as eight fork Steiner minimum tree method C/C++ of above-mentioned structure cut-through thing and be obtained through compiling.
Described automatic wiring device (112) inputs rail network structure file to be connected up to internal memory (106) by input block (102), simultaneously, the program building eight fork Steiner minimum tree methods of cut-through thing is also loaded into internal memory (106), processor performs the automatic wiring that this structure Steiner tree program (104) carries out gauze, and wire structures is supplied to user through output unit (103) in patterned mode.
Described input block (102) can be that keyboard, External memory equipment or network connect; Described output unit (103) can be display or printer.
Construction method of the present invention, first Escape figure and the grid matrix of routing planes is obtained, then decompose based on tree and merge the right angle Steiner minimum tree that heuristic thought obtains cut-through thing, make full use of 45,135 degree of newly-increased wiring trends again, introduce 5 kinds of geometric transformations, thus obtain eight fork Steiner minimum tree of the final cut-through thing needed.The present invention fast and effeciently can obtain the wiring result of eight fork Steiner minimum tree of the cut-through thing inputting gauze.
Method and apparatus tool of the present invention has the following advantages:
1., for novel X-type interconnection structure, consider again the situation that practical wiring may exist barrier simultaneously.
2. introduce the type that grid matrix concept is described in each lattice point in Escape figure, corresponding process can be made according to the type of lattice point in the geometric transformation easily below.
3. propose the right angle Steiner minimum tree of the cut-through thing obtaining the wiring of this gauze based on the decomposition of tree and the enlightening thought of merging, compared with the heuritic approach of traditional classics, more excellent result can be obtained.
4. propose 5 kinds of geometric transformations, the right angle Steiner minimum tree of cut-through thing is converted into eight fork Steiner minimum tree of cut-through thing, bus can be reduced and be about 7% ~ 15%, substantially increase wiring performance.
For the ease of understanding, by by concrete drawings and Examples, the present invention is described in detail below.It needs to be noted, instantiation and accompanying drawing are only to illustrate, obvious those of ordinary skill in the art according to illustrating, can make various correction and change to the present invention herein within the scope of the invention, and these are revised and change and also include in scope of the present invention.In addition, the present invention refer to open source literature, and these documents are to more clearly describe the present invention, and their entire contents is all included in and carried out reference herein, just looks like that repeated description is excessively the same in this article for their full text.
Accompanying drawing explanation
Fig. 1 is the theory diagram that the present invention builds eight fork Steiner minimum tree processes of cut-through thing.
Fig. 2 is the geometric transformation 1 when introducing 45,135 degree of wiring orientations in the present invention.
Fig. 3 is the geometric transformation 2 when introducing 45,135 degree of wiring orientations in the present invention.
Fig. 4 is the geometric transformation 3 when introducing 45,135 degree of wiring orientations in the present invention.
Fig. 5 is the geometric transformation 4 when introducing 45,135 degree of wiring orientations in the present invention.
Fig. 6 is the geometric transformation 5 when introducing 45,135 degree of wiring orientations in the present invention.
Fig. 7 is the structural representation that the present invention builds eight fork Steiner minimum tree devices of cut-through thing.
Fig. 8 is the right angle Steiner minimum tree structure of the cut-through thing that test case obtains.
Fig. 9 is eight fork Steiner minimum tree structures of the cut-through thing that test case obtains.
Embodiment
The representative instance that the present invention fast and effeciently builds eight fork Steiner minimum tree devices of cut-through thing is a workstation comprising 8GB internal memory, Intel Xeon3.0GHz processor and hard disk drive.Processor (109) utilizes (SuSE) Linux OS to carry out eight fork Steiner minimum tree method programs of effective fast structure cut-through thing proposed by the invention that executive routine storage unit (105) stores.
For making above-mentioned purpose of the present invention, feature and advantage more become apparent, further illustrated by following two embodiments.
Embodiment 1
Test the performance obtaining the right angle Steiner minimum tree of the cut-through thing of this gauze wiring based on the decomposition of tree and the enlightening thought of merging that step 3 of the present invention proposes, the heuritic approach of several classics of summing up in the paper delivered on Discrete Applied Mathematics with VoB S. " Steiner ' s problem in graphs:heuristic methods " compares, the test example that experiment adopts takes from OR-Library standard testing collection, obtains the test result as following table 1.Therefrom can find out, compare traditional classical heuristic algorithm DNH, MPH, what the present invention proposed can obtain more excellent wiring result based on the decomposition of tree and the algorithm of merging.
The heuristic algorithm that table 1 is more different
| Case | |V| | |E| | |X| | OPT | DNH | MPH | OURS |
| B2 | 50 | 63 | 13 | 83 | 88 | 83 | 83 |
| B10 | 75 | 150 | 13 | 86 | 94 | 89 | 86 |
| B18 | 100 | 200 | 50 | 218 | 222 | 222 | 219 |
| C1 | 500 | 625 | 5 | 85 | 88 | 87 | 85 |
| C10 | 500 | 1000 | 250 | 1093 | 1107 | 1097 | 1095 |
| C13 | 500 | 2500 | 83 | 258 | 265 | 268 | 262 |
| D3 | 1000 | 1250 | 167 | 1565 | 1615 | 1594 | 1568 |
| D9 | 1000 | 2000 | 250 | 1448 | 1504 | 1481 | 1461 |
| D17 | 1000 | 25000 | 10 | 23 | 26 | 24 | 23 |
| E5 | 2500 | 3125 | 1250 | 8128 | 8172 | 8160 | 8135 |
| E7 | 2500 | 5000 | 10 | 145 | 162 | 163 | 145 |
| E20 | 2500 | 62500 | 1250 | 1342 | 1353 | 1353 | 1349 |
Embodiment 2
The wiring line length that effective fast eight fork Steiner minimum tree methods building cut-through thing that test the present invention proposes obtain, compares with the right angle Steiner minimum tree line length of traditional cut-through thing.Wherein testing example is stochastic generation on the routing planes of 10000 × 10000.According to the number of endpoint generated and barrier number grouping test, often organize test 20 examples and be averaged.Obtain the test result as following table 2.Wherein N, M represent number of endpoint to be connected and barrier number respectively.V, E represent number of vertex and the limit number of Escape figure.L1 represents the line length of the right angle Steiner minimum tree of traditional cut-through thing, and L2 represents the line length of eight fork Steiner minimum tree of the structure cut-through thing that the present invention proposes.Therefrom can find out, the line length of eight fork Steiner minimum tree of the cut-through thing that the present invention builds, compared to the right angle Steiner minimum tree of traditional cut-through thing, can reduce bus and be about 7% ~ 15%, substantially increase the performance of wiring.
Table 2 compares two kinds of Steiner minimum tree line lengths
The right angle Steiner minimum tree of cut-through thing and eight fork Steiner minimum tree structures of cut-through thing when result has shown (respectively as shown in Figure 8 and Figure 9) one of them test case (N=50, M=20).
Claims (6)
1. a construction method for eight fork Steiner minimum tree of cut-through thing, it is characterized in that, it comprises step:
Step 1: the rail network structure file of input circuit,
Step 2: the Escape figure and the grid matrix that obtain routing planes corresponding to described gauze,
Step 3: utilize the decomposition of figure, the structure of Steiner tree and folding to obtain the right angle Steiner minimum tree of cut-through thing of described gauze wiring,
Step 4: the right angle Steiner minimum tree obtained for step 3, utilizes 45,135 degree of trends that connect up, carries out 5 kinds of basic geometric transformations,
Step 5: the eight fork Steiner minimum tree obtaining cut-through thing, and carry out global optimization, reduce the line length of wiring.
2. the method for claim 1, is characterized in that: the right angle Steiner minimum tree of the acquisition cut-through thing described in step 3, as follows:
Step 31: the trimming collection utilizing figure, is several strongly connected componentses by diagram root, and carries out the simplification of this figure,
Step 32: in each strongly connected components that step 31 obtains, build initial Steiner minimum tree,
Step 33: in each strongly connected components, carries out subtree decomposition and merging, optimizes initial Steiner minimum tree,
Step 34: connect the Steiner minimum tree in all strongly connected componentses that above-mentioned steps obtains with trimming collection, the right angle Steiner minimum tree of the cut-through thing of the routing planes described in acquisition.
3. method as claimed in claim 2, is characterized in that: in each strongly connected components, build initial Steiner minimum tree described in step 32, comprises the steps:
Step 321: choose on figure and spend two maximum summits as initial tree T
1and T
2,
Step 322: choose in residue summit, distance T
1or T
2nearest summit, joins T along its shortest path
1or T
2on, and upgrade T thus
1and T
2,
Step 323: if it is untreated to there is summit, turn to step 322, otherwise, utilize T
1and T
2between shortest path connect T
1and T
2, obtain complete Steiner minimum tree.
4. the device of eight fork Steiner minimum tree of the structure cut-through thing based on claim 1 or 2 or 3 either method, it is characterized in that, described device comprises input block (102), output unit (103), program storage unit (PSU) (105), external bus (110), internal memory (106), memory management unit (107), input and output bridge-jointing unit (108), system bus (111) and processor (109), wherein, described input block (102), output unit (103) and program storage unit (PSU) (105) are directly connected to described external bus (110), external bus (110) is connected with described system bus (111) by input and output bridge-jointing unit (108), described internal memory (106) is connected to system bus (111) by memory management unit (107),
Described processor (109) is directly connected to system bus (111).
5. by device according to claim 4, it is characterized in that, in described program storage unit (PSU) (105), store the program module (104) of the method for eight fork Steiner minimum tree of the structure cut-through thing as described in claim 1 or 2 or 3.
6. by device according to claim 4, it is characterized in that, during wiring, the rail network structure file of circuit is transferred to shown device by input block (102), and described device externally exports the wire structures of eight fork Steiner minimum tree of the cut-through thing built by output unit (103).
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| CN108804811A (en) * | 2018-06-07 | 2018-11-13 | 福州大学 | Multilayer is around barrier right angle wiring method in VLSI Design |
| CN110795907A (en) * | 2019-09-30 | 2020-02-14 | 福州大学 | X-structure Steiner minimum tree construction method considering wiring resource relaxation |
| WO2021227463A1 (en) * | 2020-05-14 | 2021-11-18 | 福州大学 | Two-step x-architecture steiner minimum tree construction method |
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| CN1540554A (en) * | 2003-10-31 | 2004-10-27 | 清华大学 | Time delay driving method of right angle Steiner tree under obstruction when making loose routing for standard units |
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| CN107832519A (en) * | 2017-11-02 | 2018-03-23 | 福州大学 | High-performance X architecture multilayer loose routing method in super large-scale integration |
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| CN108804811A (en) * | 2018-06-07 | 2018-11-13 | 福州大学 | Multilayer is around barrier right angle wiring method in VLSI Design |
| CN108804811B (en) * | 2018-06-07 | 2021-11-30 | 福州大学 | Multilayer barrier-bypassing right-angle wiring method in large-scale integrated circuit design |
| CN110795907A (en) * | 2019-09-30 | 2020-02-14 | 福州大学 | X-structure Steiner minimum tree construction method considering wiring resource relaxation |
| WO2021227463A1 (en) * | 2020-05-14 | 2021-11-18 | 福州大学 | Two-step x-architecture steiner minimum tree construction method |
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