TWI511543B - Work division method and system for improving worst waiting time - Google Patents

Description

Work division method and system for improving worst waiting time

The present invention relates to a data allocation technique for multiple channels broadcasting, and more particularly to a job partition for improving the worst waiting time. Method and system.

In a wireless communication environment, broadcasting is an effective way to simultaneously transmit data to a large number of clients. In fact, compared to the cold data item, the hot item is often accessed by the client, which is called skewed data access. Most of the current research prefers to process the hot item first. , designed to reduce the client's average waiting time (average waiting time), however, this sacrifices the interests of a small number of clients, that is, the client waiting for the unpopular data item may wait longer; in addition, this type of information Allocation or work partitioning is usually extremely time consuming (NP-hard), which requires a lot of run time for data distribution or work partitioning.

An existing data distribution technology for multi-channel broadcasting, such as "Optimal Skewed Data Allocation on Multiple Channels with Flat Broadcast" published by Elia Ardizzoni et al . in IEEE Transactions on Computers. VOL.5 No. 5. According to the per channel paper, it is assumed that the demand probability of each accessed item is available, and the data is allocated according to the demand probability of the data item. A best solution is to minimize the "average waiting time" of the client. However, the above-mentioned prior art does not consider how to improve the "waiting time of the client accessing the unpopular data item".

Another existing data distribution technology for multi-channel broadcasting, such as "Broadcast Data Allocation for Efficient Access of Multiple Data Items in Mobile Environments" published by Guanling Lee et al. in Mobile Networks and Applications 8, 365-375, 2003. As disclosed, it proposes three methods to improve the "average waiting time" of the client, namely the Pure Frequency Method, the Frequency/Size Ratio Method, and the Frequency/Size with Overlapping Method, which are considered in addition to the client's query (query). In addition to the frequency of demand for data items, there is also a measure of the amount of data to be queried. However, the above existing technology uses "the entire query" as the smallest processing unit in the data distribution process, and does not allow the "disposal of the query into several sub-collections" in the data distribution process.

Accordingly, a first object of the present invention is to provide a work division method for improving the worst wait time.

Thus, the present invention is directed to a work partitioning method for improving the worst latency, which is suitable for allocating N data items to C channels for broadcasting, wherein a data set formed by the data items is represented as D = { d ₁ , d ₂ ,..., d _N }, the method is implemented by a computer and comprises the following steps: (A) receiving m query sets from at least one client, wherein Q _i represents an i th query set For i =1, 2,..., m , Q _i D , the set of queries forms a set of query data sets and is denoted as AP ( m )={ Q ₁ , Q ₂ ,..., Q _m }; (B) according to the query sets of the query data collection group Initializing a work division result, wherein the work division result includes C jobs respectively corresponding to the channels, and the work division result is expressed as π = { P ₁ , P ₂ , ..., P _C }, P _i represents The i- th job, P _i includes the data item of the query set to which it is assigned, , | P _i | represents the number of data items included in the i- th work. The initialized work division result satisfies the following work size order: | P ₁ | | P ₂ | ... | P _C |; (C) use P _{C - β +1} , P _{C - β +2} ,..., P _C as the β candidate work in the latter stage, as the data item exceeding the work in the previous stage. Wherein, β is a preset candidate threshold; (D) determining whether there is a query set and work satisfying a preset adjustment condition, wherein the adjustment condition is: moving the query set from P ₁ to the One of the candidate jobs, P _j , j { C - β +1, C - β +2,..., C }, such that the number of | P ₁ | is reduced by the current maximum, and at the same time the number of additions of | P _j | is currently the least; E) If the result of the determination in step (D) is YES, perform the following sub-steps: (e-1) moving the query set that meets the adjustment condition from P ₁ to the work P _j ; (e-2) adjusting the work division The result is adjusted to match the size of the work: | P ₁ | | P ₂ | ... | P _C |; and (e-3) return to the judgment of step (D); (F) if the judgment result of the step (D) is no, fine-tune according to a fine-tuning rule; and (G) if the step (F) The fine-tuning result is unsuccessful, that is, it cannot be fine-tuned according to the fine-tuning rule, and the work division result at this time is used as an approximate optimal work division result, wherein the approximate optimal work division result is used as The basis for the distribution of such items to these channels for broadcast.

A second object of the present invention is to provide a work partitioning system for improving the worst waiting time.

Thus, the present invention is directed to a work partitioning system for improving the worst latency, which is suitable for distributing N data items to C channels for broadcasting, the system comprising a work partition processing module, and for storing the data items. A storage unit, the work partitioning processing module is programmed to perform a work partitioning method for improving the worst latency as described above.

A third object of the present invention is to provide a work division method for improving the worst wait time.

Thus, the present invention is directed to a work partitioning method for improving the worst latency, which is suitable for allocating N data items to C channels for broadcasting, wherein a data set formed by the data items is represented as D = { d ₁ , d ₂ ,..., d _N }, the method is implemented by a computer and comprises the following steps: (A) receiving m query sets from at least one client, wherein Q _i represents an i th query set , | Q _i | represents the number of data items included in the i- th query set, for i =1, 2,..., m , Q _i D , and all | Q _i | are the power of 2, and the query sets are not related to each other, and the query sets form a query data set and are represented as AP ( m )={ Q ₁ , Q ₂ ,..., Q _m }; (B) select the query set whose largest number of data items is the largest from the query data collection group, and n _k represents the number of data items of the selected query set; (C) Calculating an optimal waiting time according to n _k , increasing the current optimal waiting time ε ^{* by} n _k , that is, ε ^* = ε ^* + n _k ; (D) querying the query data set according to the optimal waiting time The set is assigned to C jobs of a job partitioning result, P _j represents the jth job, and P _j includes the data items of the query set to which it is assigned, wherein step (D) includes the following substeps: (d-1) Taking the jth work as the current work in progress, sequentially assigning the query sets to the work currently being processed; (d-2)| P _j | represents the number of data items included in the jth work, when present The number of data items of the data items included in the work in process is equal to the optimal waiting time, that is, when | P _j |= ε ^* The work in the process is changed to the next work, that is, j = j +1; (d-3) the sub-steps (d-1) to (d-2) are repeatedly executed until the preset first termination condition is established; E) updating the query data collection group to the remaining query set not allocated in step (D); and (F) repeating steps (B) to (E) until the preset second termination condition is established, and The work division result at this time is used as an optimal work division result, wherein the best work division result is used as a basis for allocating the data items to the channels for broadcasting.

A fourth object of the present invention is to provide a work partitioning system for improving the worst waiting time.

Thus, the present invention is directed to a work partitioning system for improving the worst latency, which is suitable for distributing N data items to C channels for broadcasting, the system comprising a work partition processing module, and for storing the data items. A storage unit, the work partitioning processing module is programmed to perform a work partitioning method for improving the worst latency as described above.

1‧‧‧Work division system

11‧‧‧ storage unit

12‧‧‧Operation mode decision module

13‧‧‧Work division processing module

130‧‧‧heuristic algorithm unit

131‧‧‧Initial unit

132‧‧‧Adjustment unit

133‧‧‧deterministic algorithm arithmetic unit

201~212‧‧‧Steps

301~302‧‧‧Steps

401~413‧‧‧Steps

Other features and effects of the present invention will be apparent from the following description of the drawings, wherein: FIG. 1 is a block diagram illustrating a preferred embodiment of the work partitioning system of the present invention for improving the worst latency. 2 is a flow chart illustrating the steps performed by a work partitioning processing module in a first computing mode in the working partitioning method for improving the worst latency; FIG. 3 is a schematic diagram illustrating The working division method for improving the worst waiting time of the present invention uses an exchange pair to divide the result of a job. An example of fine tuning; FIG. 4 is a flow chart illustrating steps performed by the working partitioning processing module in a second computing mode in the working partitioning method for improving the worst latency; and FIG. It is a flowchart illustrating the steps performed by the work partitioning processing module in a third operation mode in the work partitioning method for improving the worst latency.

The above and other technical contents, features and advantages of the present invention will be apparent from the following detailed description of the preferred embodiments.

Before the present invention is described in detail, it is noted that in the following description, similar elements are denoted by the same reference numerals.

Referring to Figure 1, the preferred embodiment of the work partitioning system 1 for improving the worst latency is applied to a wireless communication environment and is adapted to assign N data items of the same size to the C. Channels for broadcasting. The work partitioning system 1 includes a storage unit 11, an operation mode determination module 12, and a work division processing module 13.

The storage unit 11 is configured to store the data items; the operation mode determining module 12 receives m query sets from at least one client, and determines the working partition processing module 13 accordingly. The operation division processing module 13 includes a heuristic algorithm operation unit 130 having an initialization unit 131 and an adjustment unit 132, and a deterministic algorithm operation unit 133; The work partitioning processing module 13 receives the query sets, and determines the operation mode determined by the module 12 and the query sets according to the operation mode to obtain a near-optimal work partition result or a most Optimal work partitioning result; the approximate best work partitioning result or the best working partitioning result is used as a basis for allocating the data items to the channels for broadcasting.

In the preferred embodiment, the storage unit 11 is implemented as a database (not shown), and the operation mode determining module 12 and the working partition processing module 13 are implemented in a software manner. The program is a broadcast scheduling program, and when it is loaded into a computer (not shown) and executed, the working division method for improving the worst waiting time of the present invention can be implemented.

Before further describing the following, some notations to be used are defined as follows: d _i represents the i- th data item in the data items, i =1, 2, ..., N ; D represents the A set of data formed by data items, expressed as D = { d ₁ , d ₂ , ..., d _N }; Q _i represents the ith query set in the set of queries, for i =1, 2 ,..., m , Q _i D , and ; | Q _i | represents the number of data items included in the i- th query set; AP ( m ) represents a query data set pattern formed by the query sets, which is represented as AP ( m )={ Q ₁ , Q ₂ , . . . , Q _m }; π represents a work partitioning result according to the allocation of the query sets, which is expressed as π = { P ₁ , P ₂ , . . . , P _C }, wherein P _i represents the i- th job (job partition), that is, the data item of the query set to be broadcast by the i- th channel, and , ie, P _i includes the data item of the set of queries to which it is assigned, ; and | P _i | represents the number of data items included in the i- th work, that is, the number of data items to be broadcast by the i- th channel.

The work division method for improving the worst wait time of the present invention comprises the following steps.

First, the operation mode determining module 12 receives the query sets and determines the operation mode of the work partition processing module 13; the decision principle of the decision is as follows: if at least one consecutive one can be found from the query data set group The connected component determines that the operation mode of the work partition processing module 13 is a first operation mode, and the continuous associated component is defined as → →...→ ,among them, If the query sets of the query data collection group are not associated with each other (disjoint), and not all of the | Q _i | are powers of 2, then the work division processing module is determined. The operation mode of 13 is a second operation mode; otherwise, that is, all the query sets of the query data collection group are not associated with each other, and all | Q _i | are 2 powers, then the work is determined. The operation mode of the division processing module 13 is a third operation mode.

Then, the work division processing module 13 determines the operation mode determined by the module 12 and the query sets according to the operation mode to obtain the approximate optimal work division result or the optimal work division result, where The first and second computation modes mainly use the heuristic algorithm to obtain the approximate optimal work division result, which is based on the following five heuristic rules (Heuristic 1~5); the third operation mode mainly uses the deterministic algorithm. To get the best work division result, it is based on the following three auxiliary theorems (Lemma 1~3). In the present specification, the proof of the heuristic rule and the auxiliary theorem is omitted.

Heuristic 1~5 are described as follows:

[Heuristic 1]: The associated (overlapped) query set is preferably assigned to the same job.

[Heuristic 2]: For a query set whose number of data items is large, even if these query sets are in the same continuous association element, they must be allocated apart.

[Heuristic 3]: If there are unrelated query sets whose number of data items is small in the query set, the query sets are one by one in descending order (the descending order) By one) is assigned to a job whose number of items is small.

[Heuristic 4]: In the process of seeking the approximate optimal work division result, try to find a certain query set Q ^{( k )} from P ₁ for each work division result obtained by temporary (temporary ⁾ , and It is assigned to an appropriate job in the work with a smaller number of items in the work division result.

[Heuristic 5]: Q ^{( k ) is} preferably a set of queries that are not associated with other query sets.

Lemma 1~3 are described as follows:

[Lemma 1]: Let a set of integers A = { a ₁ , a ₂ ,..., a _m }, where, for i =1, 2,..., m , a _i {2 ⁰ , 2 ¹ ,...,2 ^{k -1} }; if a ₁ a ₂ ... a _m and , there is a unique integer r that makes .

[Lemma 2]: Let an AP ( m ) meet | Q ₁ | | Q ₂ | ... | Q _m |, and let ε ^* be an optimal waiting time in the third mode, and n ₀ = Max {| Q ₁ |, | Q ₂ |,..., | Q _m |}=| Q ₁ |;if , then there are C unrelated subsets S _{i in} accordance with | S _i |= n ₀ , i =1, 2, ..., C .

[Lemma 3]: Let ε _{k be} the optimal waiting time for the kth operation in the third mode, and let Where Q _i belongs to the set of query data sets at the kth operation in the third mode, ie, Q _i AP ( m - r ₁ - r ₂ -...- r _k ); , then ε _k = n _k .

The following describes the first, second, and third arithmetic modes.

First operation mode

Referring to FIG. 1 to FIG. 3, in the first operation mode, the step performed by the work division processing module 13 is further divided into an initialization phase (initial) performed by the initialization unit 131 of the heuristic algorithm operation unit 130. Phase), and a tuning phase performed by the adjusting unit 132 of the heuristic algorithm operation unit 130; The initialization phase is based on Heuristic 1~3, which includes steps 201-205; the adjustment phase is based on Heuristic 4~5, which includes steps 206-212.

In step 201, the initial work of the work division result is set, and P ₁ = P ₂ =...= P _C = These jobs correspond to the channels, respectively.

In step 202, the query for data collection Group | Q _i | The query set of α is equally distributed to the work of the work partition result, where α is a preset set size threshold.

In step 203, at least one consecutive associated element is found from the set of remaining queries in the set of query data sets that are not allocated in step 202.

In step 204, the query set belonging to the same continuous associative component among the consecutive associated components found in step 203 is assigned to the same work, and the assigned work partitioning result is adjusted to satisfy a work size order: | P ₁ | | P ₂ | ... | P _C |.

In step 205, the remaining query sets that are not allocated in step 204 in the query data collection group are allocated to the work of the work division result, and the assigned work division result is adjusted to meet the work. Sort by size: | P ₁ | | P ₂ | ... | P _C |, P _i includes the data items of the set of queries to which it was assigned during the initialization phase.

In step 206, P _{C - β +1} , P _{C - β +2,} ..., P _{C are} used as β candidates for the latter stage, where β is a predetermined candidate threshold.

In step 207, it is determined whether there is satisfied a set of queries adjustment condition Q ^(k) and work P _j, wherein the conditions are adjusted as follows: P ₁ from this set of queries Q ^(k) where the work moved to the plurality of candidate a P _j , j { C - β +1, C - β +2,..., C }, such that the number of | P ₁ | is reduced by the current maximum, and at the same time the number of | P _j | is increased to the least; If the result of the determination in step 207 is YES, then the process proceeds to step 208. Otherwise, the process proceeds to step 210.

In step 208, a set of queries Q in line with the adjustment condition ^(k) from P ₁ moves to meet the conditions for adjusting P _j.

In step 209, the work division result is adjusted to be adjusted to satisfy the work size order: | P ₁ | | P ₂ | ... | P _C |, then return to the judgment of step 207.

In step 210, the fine adjustment is performed according to a fine adjustment rule. In the preferred embodiment, the work division result is fine-tuned by using a substitute pair, and the work division result in the fine adjustment process still needs to be maintained. Work size sorting: | P ₁ | | P ₂ | ... | P _C |. Wherein the exchange pair is represented by ( Q ^r , Q ^v ), Q ^{r is} one of the query sets within the candidate jobs, or a union of the plurality of query sets within the candidate jobs, and Q ^v is a virtual query set, which is a subset of one of the query sets Q _i of P ₁ . In this fine tuning process, Q _j ( i ≠ j ) and difference set Q _i - Q ^{v in} P ₁ are first exchanged with Q ^r , and then the difference set Q _i - Q ^{v is} moved to the candidate jobs. The work with a small number of data items, after the fine-tuning process is finished, merges Q ^v into the original Q _i . Wherein the difference between the set Q _i - the set of data items Q _i Q ^v Q ^v deducted representatives.

In step 211, if the result of the fine adjustment of step 210 is successful, that is, the exchange may be used to further fine-tune the work division result while maintaining the work size ranking, then return to the judgment of step 207, otherwise (ie, , it is impossible to fine-tune according to the fine-tuning rule), and the processing proceeds to step 212.

Steps 210 to 211 are further described in conjunction with an example, as shown in (a) to (d) of FIG. 3, in this example, β = 2. Prior to trimming, the result of dividing the work of FIG. 3 (a),; wherein the P ₁ of a query set _{Q 2 = {d 1, d} 2} is split out a subset of Q ^v = {d _2} And Q ₂ - Q ^v = { d ₁ }; then, as shown in (b) to (c) of FIG. ₃ , Q ₁ and Q ₂ - Q ^{v in} P ₁ , and Q ^{r in} the candidate work Exchange, where, Tian Yu | Q ₁ ∪ Q ₂ |=| Q ^r ∪ Q ^v |, so the result of the work division after the exchange will maintain the work size order: | P ₁ | | P ₂ | ... | P _C |; Finally, as shown in (d) of FIG. 3, Q ^{v is} merged into the original Q ₂ .

In step 212, the work division result at this time is used as the approximate best work division result, and an approximate optimal "worst wait time" corresponding to the approximate best work division result is | P ₁ |, That is, the time required for the first channel to broadcast all data items.

Second operation mode

Referring to FIG. 1 and FIG. 4, in the second operation mode, the step performed by the work division processing module 13 is substantially similar to the first operation mode, and is divided into an initialization unit by the heuristic algorithm operation unit 130. An initialization phase performed by 131, and an adjustment phase performed by the adjustment unit 132 of the heuristic algorithm operation unit 130; wherein the steps of the initialization phase are slightly different from the first operation mode, wherein the query set The two-two are not associated, which is simplified to include steps 301, 302; and the steps of the adjustment phase are similar to the first operational mode; the following is only described with slightly different initialization phases.

In step 301, the C jobs of the work division result are initially set, and P ₁ = P ₂ =...= P _C = .

In step 302, the query set of the query data collection group is allocated to the work of the work division result, and the assigned work division result is adjusted to meet the work size order: | P ₁ | | P ₂ | ... | P _C |.

Third operation mode

Referring to FIG. 1 and FIG. 5, in the third operation mode, two or two unrelated query sets are processed, and the query set size is a power of 2, and the deterministic algorithm operation unit 133 performs the following steps.

In step 401, the query set of the query data collection group is sorted, and the sorted query data collection group AP ( m )={ Q ₁ , Q ₂ , . . . , Q _m } is in accordance with | Q ₁ | | Q ₂ | ... | Q _m |.

In step 402, the initial work of the work division result is set, and P ₁ = P ₂ =...= P _C = These jobs correspond to the channels, respectively.

In step 403, an initial query set index (represented by i ), an operation count (iteration, denoted by k ), and an optimal wait time (represented by ε ^* ), i =1, k =0, and ε ^* =0.

In step 404, a query set whose number of items is the largest is selected from the set of query data sets, and n _k represents the number of items of the selected set of queries, that is, n _k =| Q _i |.

In step 405, the waiting time is calculated according to the approximate optimum n _k, the presently preferred incremental latency ε ^* n _k, i.e., ε = ε + n _k.

In step 406, a work index (indicated by j ) indicating the work in the current process is set, j =1.

In step 407, Q _{i is} assigned to the currently processed work P _j , P _j including the data item of the query set to which it is assigned.

In step 408, the query set index is updated, ie, i = i +1 is set.

In step 409, when the number of data items included in the currently processed work is equal to the optimal waiting time, that is, when | P _j |= ε ^* , the current processing work is changed to the next work, that is, , set j = j +1.

In step 410, it is determined whether a preset first termination condition is established, wherein the first termination condition is: all the query sets have been assigned to the work (ie, i > m ), or all work has been Assigned to at least one query set (ie, j > C ); if the first termination condition has not been established, then returns to step 407, otherwise, proceeds to step 411 to continue processing.

In step 411, it is determined whether a preset second termination condition is established, wherein the second termination condition is: all the query sets have been assigned to the work (ie, i > m ); if the second termination If the condition has not been established, then processing continues to step 412, otherwise, processing continues to step 413.

In step 412, the number of operations is updated, i.e., k = k +1 is set; and the set of query data sets is updated to the remaining set of queries that are not allocated; then, returning to step 404, processing continues.

In step 413, the work division result at this time is taken as the best work division result, and the optimal "worst wait time" corresponding to the optimal work division result is ε ^* =| P ₁ |= n ₀ + n ₁ +... n _k .

Finally, the work partitioning processing module 13 outputs the best work partitioning result as a basis for distributing the data items to the channels for broadcasting.

In summary, the method and system proposed by the present invention do not obtain an optimal solution for data distribution based on the "demand probability of the accessed data item". Therefore, for a client that needs an unpopular data item, The required waiting time (also known as the worst waiting time) can be improved; furthermore, the method and system proposed by the present invention can solve the extremely time-consuming work assignment problem in an efficient manner, and even existing In the technology, "the contents of the query set that cannot be processed separately are temporarily separated", and the concept of the exchange pair and its virtual query set are fine-tuned, so that the object of the present invention can be achieved.

The above is only the preferred embodiment of the present invention, and the scope of the present invention is not limited thereto, that is, the simple equivalent changes and modifications made by the patent application scope and patent specification content of the present invention, All remain within the scope of the invention patent.

401~413‧‧‧Steps

Claims (4)

A work division method for improving the worst wait time, which is suitable for distributing N data items to C channels for broadcasting, wherein a data set formed by the data items is represented as D = { d ₁ , d ₂ ,..., d _N }, the method is implemented by a computer and includes the following steps: (A) receiving m query sets from at least one client, and defining Q _{i to} represent the i- th query set, | Q _i | represents the number of data items included in the i- th query set, for i = 1, 2, ..., m , Q _i D , and all | Q _i | are the power of 2, and the query sets are not related to each other, and the query sets form a query data set and are represented as (B) selecting the query set whose largest number of data items is the largest from the query data collection group, n _k represents the number of data items of the selected query set; (C) calculating an optimal waiting time according to n _k , which will present The optimal waiting time ε ^{* is} incremented by n _k , that is, ε ^* = ε ^{* +} n _k ; (D) assigning the query set of the query data set to the C work of a work division result according to the optimal waiting time, The jobs correspond to the channels, respectively, P _j represents the jth job, P _j includes the data items of the set of queries to which they are assigned, wherein step (D) includes the following sub-steps: (d-1) to j Work as the current work in progress, sequentially assigning the set of queries to the work currently being processed; (d-2)| P _j | represents the number of data items included in the jth work, when currently in process When the number of data items of the data item included in the work is equal to the optimal waiting time, that is, when | P _j |= ε ^* , the current work in progress is changed to the next work, that is, j = j +1; (d-3) repeatedly performing sub-steps (d-1) to (d-2) until a preset first termination condition is established; (E Updating the query data collection group to the remaining query sets not allocated in step (D); and (F) repeating steps (B) to (E) until a preset second termination condition is established, and The work division result at this time is used as an optimal work division result, wherein the best work division result is used as a basis for allocating the data items to the channels for broadcasting. The work division method for improving the worst waiting time as described in claim 1 further includes a step (G) before step (B): (G) performing the following initialization: initializing the work division result into C empty Work and set the approximate optimal wait time to 0, ie, ε ^* =0. The work division method for improving the worst wait time as described in claim 1, wherein the first termination condition described in the sub-step (d-3) is: all the query sets are allocated to the work, Or all work has been assigned to at least one query set, and the second termination condition described in step (F) is that all of the query sets have been assigned to the work. A work partitioning system for improving the worst waiting time, which is suitable for distributing N data items to C channels for broadcasting, the system comprising a work partition processing module, and a storage unit for storing the data items The work division processing module is planned to perform the work division method for improving the worst wait time as described in any one of claims 1 to 3.