C. J. Alpert and A. B. Kahng, "Recent directions in netlist partitioning: a survey," Integration, VLSI J., pp. 1--81, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....i.e. the statement that if the cut due to relation qj is higher than the cut due to relation qi, the cost of qj is lower than the cost of qi is not always true. For example if we look for an allocation to 4 disks, and if two relations qi and qj of size 5 are distributed among these 4 disks as [2 1 1 1] and [2 2 1 0] respectively, the cut due to q will be higher than the cut due to qj although the retrieval times of these two relations are the ql= dl, d2, d3 q4= d2, d4 Disk I . Disk I Disk 2 Disk 2 Database System 1 st partition of WSG 2nd partition of WSG ....

....that if the cut due to relation qj is higher than the cut due to relation qi, the cost of qj is lower than the cost of qi is not always true. For example if we look for an allocation to 4 disks, and if two relations qi and qj of size 5 are distributed among these 4 disks as [2 1 1 1] and [2 2 1 0] respectively, the cut due to q will be higher than the cut due to qj although the retrieval times of these two relations are the ql= dl, d2, d3 q4= d2, d4 Disk I . Disk I Disk 2 Disk 2 Database System 1 st partition of WSG 2nd partition of WSG Figure 2.1: ....

[Article contains additional citation context not shown here]

C. J. Alperr and A. B. Kahng. Recent directions in netlist partitioning: A survey. VLSI Journal, 19(1-2):1-81, 1995.

.... vertices, it is possible to find its optimal unconstrained bipartition in polynomial time by applying a max flow algorithm at most 1 times [1] However, once we require the two circuit parts be of approximately equal size, the problem becomes hard, and we have to resort to heuristics [2, 3]. Note that circuit part size constraints are completely different from our constraint, while circuit bipartitioning cost is a special case of our cost function. In [4] the authors applied network flows to circuit partitioning for reconfigurable FPGAs. The input to the problem is a directed ....

C. Alpert and A. Kahng, "Recent directions in netlist partitioning: A survey," Integration: VLSI J., vol. 19, 1995.

.... cuts can be easily approximated using it [11, 17] Also several other important approximation algorithms like crossing number and minimum cut linear arrangement are based on the ratio cut [11] Ratio cut has many practical applications, most important being VLSI design, clustering and partitioning [20, 12, 1 ]. Since ratio cut is a NP hard problem [13] we must seek for approximation algorithms to solve it in practically reasonable time. Many purely heuristic algorithms were developed [20, 22, 18, 6] most of them relying on simulated annealing, spectral methods or iterative movement of nodes from one ....

C.J. Alperr and A. Kahng, Recent directions in netlist partitioning: a survey, tech. report, Computer Science Department, University of California at Los Angeles, 1995.

.... cuts can be easily approximated using it [13, 20] Also several other important approximation algorithms like crossing number and minimum cut linear arrangement are based on the ratio cut [13] Ratio cut has many practical applications, most important being VLSI design, clustering and partitioning [23, 14, 1]. Since ratio cut is a NP hard problem [15] we must seek for approximation algorithms to solve it in practically reasonable time. Many purely heuristic algorithms were developed [23, 25, 21, 8] most of them relying on simulated annealing, spectral methods or iterative movement of nodes from one ....

C. J. Alpert and A. Kahng, Recent directions in netlist partitioning: a survey, tech. report, Computer Science Department, University of California at Los Angeles, 1995.

....trade o# in terms of the number and importance of application domains and suitability for optimization. Kernighan and Lin introduced the first iterative improvement heuristic and applied it to graph partitioning [3] Numerous improvements on the basic strategies have been proposed over the years [1]. Iterative improvement has been also applied to many other optimization problems [6] 3. PRELIMINARIES We have chosen as a computational model the synchronous data flow( SDF) model [5] We restrict our attention to homogeneous SDF( fl1# where each atomic operational unit consumes and produces ....

C.J. Alpert and A.B. Kahng. Recent Directions in Netlist Partitioning: A Survey. Integration: The VLSI Journal Vol.19(19,fl1U pp.1--81 1995.

....problem. Then, we describe our novel and accurate GPVS based formulation for the HP problem. Finally, we provide a discussion on the matrix theoretical view of the relation between HP and GPVS problems. 7.1. Alternative Models for Solving HP Problem. As indicated in the survey by Alpert and Kahng [1], hypergraphs are commonly used to represent circuit netlist connections in solving the circuit partitioning and placement problems in VLSI layout design. The circuit partitioning problem is to divide a system specification into clusters to minimize inter cluster connections. Other circuit ....

....design. The circuit partitioning problem is to divide a system specification into clusters to minimize inter cluster connections. Other circuit representation models were also proposed and used in the VLSI literature including dual hypergraph, cliquenet graph (CNG) and net intersection graph (NIG) [1]. Hypergraphs represent circuits in a natural way so that the circuit partitioning problem is directly described as an HP problem. Thus, these alternative models can be considered as alternative approaches for solving the HP problem. The dual of a hypergraph H = U ; N ) is defined as a ....

[Article contains additional citation context not shown here]

C.J. Alpert and A.B. Kahng, "Recent Directions in Netlist Partitioning: A survey," VLSI Journal, vol. 19, nos. 1-2, pp. 1--81, 1995.

....the statement that if the cut due to relation q j is higher than the cut due to relation q i , the cost of q j is lower than the cost of q i is not always true. For example if we look for an allocation to 4 disks, and if two relations q i and q j of size 5 are distributed among these 4 disks as [2 1 1 1] and [2 2 1 0] respectively, the cut due to q i will be higher than the cut due to q j although the retrieval times of these two relations are the q2 = d1, d4 q3 = d1, d5 q4 = d2, d4 q5 = d2, d5 q6 = d3, d4 q7 = d3, d5 q1= d1, d2, d3 Disk 2 Disk 1 1 1 1 1 1 1 1 1 1 1 ....

....that if the cut due to relation q j is higher than the cut due to relation q i , the cost of q j is lower than the cost of q i is not always true. For example if we look for an allocation to 4 disks, and if two relations q i and q j of size 5 are distributed among these 4 disks as [2 1 1 1] and [2 2 1 0] respectively, the cut due to q i will be higher than the cut due to q j although the retrieval times of these two relations are the q2 = d1, d4 q3 = d1, d5 q4 = d2, d4 q5 = d2, d5 q6 = d3, d4 q7 = d3, d5 q1= d1, d2, d3 Disk 2 Disk 1 1 1 1 1 1 1 1 1 1 1 d1 d2 d3 d4 ....

[Article contains additional citation context not shown here]

C. J. Alpert and A. B. Kahng. Recent directions in netlist partitioning: A survey. VLSI Journal, 19(1-2):1--81, 1995.

....using one of the tie breaking strategies described below. The terminology used in this paper (i.e. gain, gain buckets, gain tables) is adapted from the established terminology for analogous data structures used in local search algorithms for a similar problem domain, hypergraph partitioning [1]. An index to the highest non empty gain table is maintained incrementally, so finding this entry is a constant time operation. 2.1 Tie Breaking Heuristics We now describe the tie breaking heuristics (i.e. strategy for selecting a variable out of a gain bucket) that were evaluated. Each of ....

C.J. Alpert and A.B. Kahng. Recent directions in netlist partitioning: a survey. Integration: the VLSI Journal, 19:1--81, 1995.

....search process with a populationbased approach using a genetic algorithm. Benchmark comparisons are not presented. While a number of genetic algorithms have been proposed for dealing with the partition problem, none of them are truly competitive with the state ofthe art tools in the area. [Alpert and Khang (1995)] present a fully survey on partitioning, including a number of the most sophisticated probabilistic and deterministic algorithms for the problem. For a tutorial on genetic algorithm partitioning, consider [Mazumder and Shahookar (1999) 5.2 Placement The placement step assigns physical ....

Alpert C.J. and Khang A.B. Recent Directions in Netlist Partitioning: A Survey, Integration: The VLSI Journal, vol. 19,

....need for effective and efficient IPP schemes and tools. We present a general constraint based watermarking scheme and analyize it in the context of graph partitioning. Graph partitioning is a critical optimization problem that has many applications, particularly in the semiconductor design process [1]. Our IPP technique for graph partitioning watermarks solutions to graph partitioning problems so that they carry an author s signature. The general constraint based watermarking approach maps an author s signature into a set of constraints and then modifies the partitioning objective function so ....

....(14,3) 9,8) 2. RELATED WORK The graph partitioning problem is ubiquitous in many fields of computer science and engineering. It has important applications in areas ranging from work load balancing in parallel programming, to database storage and in particular to VLSI design and CAD techniques [1]. Throughout the process of VLSI circuit design and synthesis graph partitioning plays a key role. It has applications in system design, behavioral synthesis, system level synthesis, packaging, rapid prototyping, and testing. The graph partitioning problem is NPcomplete. Therefore many heuristic ....

C. J. Alpert, A. B. Kahng. Recent directions in netlist partitioning: a survey. INTEGRATION, the VLSI Journal, pp.1-81, 1995.

....the algorithm is able to iteratively move elements from partition to partition. Many different improvements on the strategy have been proposed. The most well known being by Fiduccia and Mattheyses [Fid82] Sanchis [San89] and Krishnamurthy [Kri84] Alpert and Kahng give a survey on the topic [Alp95]. Until recently many of the probabilistic algorithms proposed were probabilistic iterative improvement algorithms. Two of the main techniques are the Metropolis algorithm [Met53] and Simulated Annealing [Kir83, Joh91] Simulated Annealing has been used for a number of applications in ....

C.J. Alpert, A.B. Kahng. Recent Directions in Netlist Partitioning: A Survey. Integration: The VLSI Journal, Vol. 19, 1995.

....or use dynamic programming. In the last three decades, deterministic iterative improvement algorithms [15] were proposed for many problems and they were able to produce the best results. In particular, deterministic iterative improvement algorithms are widely and frequently used for partitioning [2]. Since the mid 80 s, when simulated annealing was first proposed for use in designing multi chip computers [16] probabilistic iterative improvement has attracted a great deal of attention for solving CAD problems. Techniques such as Genetic Algorithms, Tabu Search, and Simulated Evolution, due ....

....pair swap moves to iteratively reassign elements to different partitions. It proceeds in a series of passes, during which each component is moved exactly once. A number of improvements on the basic strategies have been proposed over the years [10] An excellent survey of this research is given in [2]. The iterative improvement paradigm has been applied to many other optimization problems, including the traveling salesman problem [Lin73] Randomized versions of the deterministic constructive algorithms have been popular for a long time [19] Randomization often dramatically . Kernighan Lin . ....

C.J. Alpert, A.B. Kahng. "Recent Directions in Netlist Partitioning: A Survey." Integration: The VLSI Journal, vol. 19, 1995.

....k points, etc. The main difference between these problems is in the objective functions. The earlier work shows that, in general, optimum clustering is a hard problem [2] Many different heuristics have been proposed in clustering area [3] Clustering heuristics are either bottom up or top down [27]. In a bottom up approach, each block is a cluster in the beginning. Clusters are gradually merged and grouped together. Finding the best pair of clusters to merge may not be very efficient. This method is called agglormerative approach in [27] On a top down approach, several new clusters are ....

....Clustering heuristics are either bottom up or top down [27] In a bottom up approach, each block is a cluster in the beginning. Clusters are gradually merged and grouped together. Finding the best pair of clusters to merge may not be very efficient. This method is called agglormerative approach in [27]. On a top down approach, several new clusters are generated at a time. Clustering may include multiple objectives. For instance, minimizing the number of clusters and minimizing the number of external connections between clusters can be the two objectives in a clustering problem. Figure 4 shows ....

C. J. Alpert, A. B. Khang, "Recent Directions in Netlist Partitioning: A survey,". The VLSI Journal 19, pp. 1-81, 1995.

.... Although there has been wide ranges of algorithms published that address the partitioning problem for FPGAs [11 13] most of these algorithms have an objective function of dividing the netlist (or task graph) into clusters such that inter cluster communication (interconnect) is minimized [14] or the application execution delay is minimized. In selecting a partitioning algorithm for use in an OS4RC, the objective function is to have a small, deterministic and bounded algorithm run time. It must be small because (as with scheduling in a traditional OS) the run time is a direct overhead. ....

Alpert, C. and A. Kahng, Recent Directions in Netlist Partitioning: A Survey. Integration, the VLSI Journal, 1995. 19: p. 1-81.

....addressed. Possibilities for future extensions to mitigate these problems are suggested. II. Related work Mainly because of the lack of available industrial benchmarks, the research community has tried to come up with di#erent ways of generating synthetic circuits (some of them are presented in [5], p. 81) An obvious way is to select a number of logic gates and then connect the gate terminals randomly with a certain probability. Unfortunately, it is questionable if such circuits can be accepted as realistic logic circuits. For this reason, the first successful trials of benchmark ....

C. J. Alpert and A. B. Kahng, "Recent directions in netlist partitioning: a survey," Integration, the VLSI Journal, vol. 19, no. 1--2, pp. 1--81, 1995.

....with a range of edge weights, and for multi way partitioning, the iterative deletion approach can outperform the iterative improvement method. The algorithmic approach is flexible and can support complex cost functions directly. 1. INTRODUCTION The netlist partitioning problem is well known; [3] provides a recent survey of work on this problem. The common formulation involves a hypergraph H#V;E#, with n vertices V = fv1;v 2 ; v ng. Each edge e i 2 E of the hypergraph connects a subset of the vertices. If we partition the hypergraph, we determine a group of non intersecting subsets of ....

....partially supported by the SUNY Binghamton Office of Research and Sponsored Programs. our approach to a number of well known partitioning algorithms, for both bipartitioning and multi way partitioning problems. The paper concludes with some remarks in Section 6. 2. PREVIOUS WORK The survey of [3] provides four general classifications for current approaches to the traditional partitioning problem. Move based approaches are common; most begin with a randomly chosen initial partition, and iteratively move vertices between clusters to optimize the number of edges cut. Geometric approaches are ....

[Article contains additional citation context not shown here]

C. J. Alpert and A. B. Kahng. Recent directions in netlist partitioning: A survey. Integration, the VLSI Journal, pages 1--81, 1995.

....is NP complete [19] a number of approximate schemes have been proposed. These include iterative improvement methods [16, 17, 23, 24, 29, 30] simulated annealing [31, 32] and clustering based techniques [7, 5, 18, 20, 28, 29, 36, 35] An excellent survey on partitioning techniques appears in [6]. In iterative improvement, we start with a random 2 way partition of the circuit, and iteratively improve it by either swapping pairs of nodes between the subsets, or moving one node at a time between them so that the cutset size is reduced. Clustering based methods try to find natural clusters ....

C.J. Alpert and A.B. Kahng, "Recent directions in netlist partitioning: A survey", Integration, The VLSI Journal, 19(1-2), 1995, pp. 1-81.

....level becomes possible. Examples of iterative SeqLP based on quadrisection are iterative improvement [3] and cycling [4] Circuit Partitioning Engine: Circuit partitioning engines are crucial to the performance of any PDP algorithm. A comprehensive survey of circuit partitioning is given in [9]. Most state of the art bi partitioners are of the iterative improvement family, and can be regarded as variants of FM [6] which is linear time per pass. Dutt and Deng proposed two novel iterative improvement partitioners (IIPs) PROP [7] considers futuristic as well as immediate gain, while CLIP ....

C. J. Alpert and A. B. Kahng, "Recent Directions in Netlist Partitioning: A Survey," Integration, The VLSI Journal, 19(1-2), pp. 1-81, 1995.

....or use dynamic programming. In the last three decades, deterministic iterative improvement algorithms [Ker70] were proposed for many problems and were able to produce the best results. In particular, deterministic iterative improvement algorithms are widely and frequently used for partitioning [Alp95]. Since the mid 80 s, when Simulated Annealing was first proposed for use in designing multi chip computers [Kir83] probabilistic iterative improvement has attracted a great deal of attention for solving CAD problems. Techniques such as Genetic Algorithms, Tabu Search,and Simulated Evolution, ....

....each component is moved exactly once. A number of improvements on the basic strategies have been proposed over the years [Gav72] The most notable are the ones proposed by Fiduccia and Mattheyses [Fid82] Sanchis [San89] and Krishnamurthy [Kri84] An excellent survey of this research is given in [Alp95]. The iterative improvement paradigm has been applied to many other optimization problems, including the Traveling Salesman Problem [Lin73] Randomized versions of the deterministic constructive algorithms have been popular for a long time [Mot95] Randomization often dramatically improves the ....

C.J. Alpert, A.B. Kahng. "Recent Directions in Netlist Partitioning: A Survey." Integration: The VLSI Journal, vol. 19, 1995.

.... Search (HuGSS) and we have applied it successfully to the problem of capacitated vehicle routing with time windows [3] We are currently trying to apply the same general approach to the problem of k way network partitioning, an important NP hard problem that arises in VLSI design and elsewhere [2]. In this paper we demonstrate the visualization aspects of our interactive network partitioning system. The networks that we consider are derived from chip circuits modeled as hypergraphs; these hypergraphs have up to 200; 000 nodes and as many hyperedges. We need to visualize those aspects of a ....

....vary around the value n k , where n = jV j; a typical value for the allowed variance is 10 . In current state of the art benchmark problems, jV j and jH j range from 10,000 to 200,000, and k is less than 10 [1] A recent survey describes the many heuristics that have been devised for this problem [2]. Typical heuristics for difficult combinatorial optimization problems combine some form of gradient descent to find local minima with some strategy for escaping nonoptimal local minima and exploring the solution space. The HuGSS framework for interactive search [3] divides these two subtasks ....

C. J. Alpert and A. B. Kahng. Recent directions in netlist partitioning: A survey. Integration: The VLSI Journal, 19:1--81, 1995.

....at each step using the least squares deviation optimality criterion. An alternative scheme for tree generation might allow arbitrary partitions at intermediate steps (i.e. join any number of taxa rather than exactly two) In this case, a number of existing efficient partitioning heuristics [1] can be readily applied to generate more promising and diverse partial solutions. Likewise, the method for selecting topologically diverse partial solutions might select more solutions from more distant topologies, rather than uniformly sampling the topological distances as is done in this ....

C. Alpert and A. B. Kahng, Recent Directions in Netlist Partitioning: A Survey, Integration: The VLSI Journal, 19 (1995), pp. 1--81.

.... link is instantiated to connect the two pages corresponding to the subsets; the area taken up on a page is computed by summing the areas required for 4 Recent research has produced a host of new graph partitioning algorithms, some of which are demonstrably superior to the KL algorithm [1]. We used the KL algorithm because it is simple and relatively easy to modify and generalize. 5 The KL algorithm requires an initial valid partitioning as input. MERL TR 95 6 February 1995 7 DEP 25 WELCOME EXIT X BAL WD SAV X TRNSFR SAV BAL X SAV TRNSFR 20 100 50 15 15 15 15 15 15 ....

C. J. Alpert and A. B. Kahng. Recent directions in netlist partitioning: A survey. Integration: The VLSI Journal, 19:1--81, 1995.

....44 125 91 67 s38584 168 49 76 55 47 s35932 162 47 105 62 49 Geom. Mean 128.5 47.5 112.7 73.1 60.3 Normalized 2.705 1.000 2.373 1.539 1.269 Table 1. Comparison of partitioners. Partitions are between 45 and 55 of total circuit size. FM and Strawman results are from [6] EIG1 results from [1, 7], and Paraboli results from [12] The various techniques used by Strawman to achieve its superior results are outlined below. A more detailed explanation of these techniques can be found in [6] 3 . Random i nitial partitioning The initial partition is generated by randomly placing nodes into ....

C. J. Alpert, A. B. Kahng, "Recent Directions in Netlist Partitioning: A Survey", Integration: the VLSI Journal, Vol. 19, No. 1-2, pp. 1-81, 1995.

....k points, etc. The main difference between these problems is in the objective functions. The earlier work shows that, in general, optimum clustering is a hard problem [2] Many different heuristics have been proposed in clustering area [3] Clustering heuristics are either bottom up or top down [24]. In a bottom up approach, each block is a cluster in the beginning. Clusters are gradually merged and grouped together. Finding the best pair of clusters to merge may not be very efficient. This method is called agglormorative approach in [24] On a top down approach, several new clusters are ....

....Clustering heuristics are either bottom up or top down [24] In a bottom up approach, each block is a cluster in the beginning. Clusters are gradually merged and grouped together. Finding the best pair of clusters to merge may not be very efficient. This method is called agglormorative approach in [24]. On a top down approach, several new clusters are generated at a time. Clustering may include multiple objectives. For instance, minimizing the number of clusters and minimizing the number of external connections between clusters can be the two objectives in a clustering problem. Figure 6 shows ....

[Article contains additional citation context not shown here]

C. J. Alpert, A. B. Khang, "Recent Directions in Netlist Partitioning: A survey,". The VLSI Journal 19, pp. 1-81, 1995.

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C. J. Alpert and A. B. Kahng, "Recent directions in netlist partitioning: A survey," Integration, vol. 19, pp. 1--81, 1995. All implementations of this work are publicly available at http://vlsicad. cs.ucla.edu/software/PDtools/. In the worst case sense; also under the assumption of constant partitioning tolerance and legal partitioning solutions on all levels.

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C. J. Alpert and A. B. Kahng, "Recent Directions in Netlist Partitioning: A Survey", Integration, the VLSI Journal, 19(1-2) (1995), pp. 1-81. 28

....E. Row Based Placement For row based placement, traditional physical embedding constraint types (i.e. region and grouping constraints) are straightforward to realize. Region constraints are transparent to top down placers, since iterative partitioners accommodate fixed preassignments (see [2] for a review) Annealing placers (see [51] for a review) also support such constraints by restricting move generation and analytic placers support region constraints via inequalities or center of gravity constraints (see [1] for a review) Grouping constraints are typically enforced by inducing ....

C. J. Alpert and A. B. Kahng, "Recent directions in netlist partitioning: A survey," Integr. VLSI J., vol. 19, no. 1-2, pp. 1--81, Aug. 1995.

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C. J. Alpert and A. B. Kahng, "Recent directions in netlist partitioning: a survey," Integration, VLSI J., pp. 1--81, 1995.

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C. J. Alpert and A. B. Kahng. Recent directions in netlist partitioning: a survey. Integr. VLSI J., 19(1-2):1--81, 1995.

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C. J. Alpert and A. B. Kahng. Recent directions in netlist partitioning: A survey. Integration, the VLSI Journal, 19(12) :1--81, 1995.

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C. J. Alpert and A. B. Kahng. Recent directions in netlist partitioning: a survey. Integr. VLSI J., 19(1-2):1--81, 1995.

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C. J. Alpert and A. Kahng. Recent directions in netlist partitioning: A survey. VLSI Journal, 19(1--2):1--81, 1995.

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C. J. Alpert and A. B. Kahng. Recent directions in netlist partitioning: A survey. Integration, the VLSI Journal, 19(12) :1--81, 1995.

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C. J. Alpert and A. B. Kahng. Recent directions in netlist partitioning: A survey. Integration: The VLSI Journal, 19:1--81, 1995. 28

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C. Alpert and A. Kahng. Recent directions in netlist partitioning : a survey. Integration, the VLSI Journal, 19(1-2):1-- 81, 1995.

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Charles J. Alpert and Andrew B. Kahng. Recent directions in netlist partitioning: A survey. Integration, the VLSI Journal, 19(1-2):1--81, 1995.

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C. Alpert and A. Kahng. Recent directions in netlist partitioning : a survey. Integration, the VLSI Journal, 19(1-2):1-- 81, 1995.

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C. J. Alpert and A. Kahng. Recent directions in netlist partitioning: A survey. VLSI Journal, 19(1--2):1--81, 1995.

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C. J. Alpert and A. B. Kahng, "Recent direction in netlist partitioning: A survey", INTEGRATION: The VLSI J. vol. N 19, 1995, pp. 1-81.

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C.J. Alpert and A. B. Kahng, "Recent Direction in Netlist Partitioning: A Survey," INTEGRATION: the VLSI Journal, N19, pp. 1-81, 1995.

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C. Alpert and A. Kahng. Recent directions in netlist partitioning: A survey. Integration: The VLSI Journal, pages 1--81, 1995.

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C. J. Alpert and A. B. Kahng. Recent directions in netlist partitioning: A survey. Integration, the VLSI Journal, 19(1-2):1--81, 1995.

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C. J. Alpert and A. B. Kahng, "Recent direction in netlist partitioning: A survey", INTEGRATION: The VLSI J. vol. N 19, pp. 1-81, 1995.

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C. J. Alpert and A. B. Kahng, "Recent directions in netlist partitioning: a survey," Integration, VLSI J., pp. 1--81, 1995.

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C. J. Alpert and A. B. Kahng, "Recent directions in netlist partitioning: A survey," Integration, VLSI J., vol. 19, pp. 1--81, 1995.

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Charles J. Alpert and Andrew B. Kahng. Recent directions in netlist partitioning: A survey. Integration, the VLSI Journal, 19(1-2):1--81, 1995.

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C.J. Alpert and A.B. Kahng. Recent directions in netlist partitioning: A survey. INTEGRATION, the VLSI Jour., 1-2(19):1--81, 1995.

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Alpert CJ, Kahng AB. Recent directions in netlist partitioning: a survey. Integration, The VLSI Journal, 19 (1995), 1-81.

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C. J. Alpert, A. B. Khang, "Recent Directions in Netlist Partitioning: A survey,". The VLSI Journal 19, pp. 1-81, 1995.

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C. J. Alpert and A. B. Kahng, "Recent Directions in Netlist Partitioning: A Survey, " INTEGRATION: the VLSI journal, vol. 19, pp.1-81,1995.

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