C. Chekuri, A. V. Goldberg, D. Karger, M. Levine, and C. Stein. Experimental study of minimum cut algorithms. In Proc. of 8th SODA, 324--333, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....to assign a node to multiple categories, something we have also noticed in our citeseer data set. This is a more general limitation of all clustering algorithms that produce disjoint clusters. Implementation wise, maximum ow algorithms have been sped up signi cantly over the past years [6] [1], but they are still computationally intense. Randomized or approximation algorithms could yield similar results but in less time, thus laying the basis for very fast cut clustering techniques of high quality. ....

C. S. Chekuri, A. V. Goldberg D. R. Karger, M. S. Levine, and C. Stein. Experimental Study of Minimum Cut Algorithms. In Proc. 8th ACM-SIAM Symposium on Discrete Algorithms, pages 324{ 333, 1997.

....n pixels in each of the three images and we restrict our solutions to d possible disparity levels, then the spatial complex has nd voxels. With two way faces included, this results in 10nd cells and 20nd faces; the dual graph has correspondingly many vertices and edges. Using known flow algorithms [5], this leads to a worst case time complexity of O( nd) log(nd) 6 Implementation and Results We have coded our minimal cost surface stereo algorithm and tested it on a number of datasets. An example of our rectification is shown in Figure 9. On the left is the three original images. On the ....

C. Chekuri, A. Goldberg, D. Karger, M. Levine, and C. Stein. Experimental study of minimum cut algorithms. Proc ACM SODA, 1997.

.... the maximum number of back edges on any acyclic path in G f l and typically d 6 3 in practical cases [24] The min cut step of our algorithm operates on the reduced graph G rd = N rd ; E rd ; W rd ) There are a variety of polynomial algorithms in the literature with different time complexities [11]. In our implementation, we have used Goldberg s push relabel HIPR algorithm since it has been reported to be efficient with its worst time complexity being O(jN rd j p jE rd j) 17] Hence, MC PRE has a polynomial time complexity overall. In Section 4, we discuss the compile time overhead of ....

C. Chekuri, A. V. Goldberg, D. R. Karger, M. S. Levine, and C. Stein. Experimental study of minimum cut algorithms. In ACM/SIAM Symposium on Discrete Algorithms, pages 324-- 333, 1997.

....led to a recent increase in the experimental study of algorithms. There have been a number of experimental studies of graph algorithms which focus on important problems such as shortest paths [9, 5] minimum spanning trees (MST) 17] network ow and matching [1, 4, 10, 19] and min cut algorithms [6]. These experiments provide valuable insight into the performance of di erent algorithms and can suggest new algorithmic choices. The authors of these studies reasonably spend most of their e ort on the higher level algorithm details, so these papers have typically had a very limited discussion of ....

C. Chekuri, A. Goldberg, D. Karger, M. Levine, and C. Stein, Experimental study of minimum cut algorithms. Technical Report 96-132, NEC Research Institute, Inc., October 1996.

....a given network will fail [3, 6] This was done by enumerating the approximately minimum cuts in the network, and it was proved that the probability that the network will fail can be approximated using this enumeration. The problem of enumerating approximately minimum cuts has been dealt with in [1, 4, 5]. Another objective studied for probabilistic graphs is to determine the most reliable source in a given network or graph. Linear time algorithms exist for this problem when the graph is a tree [10] or a series parallel graph [2] The problem that has been considered in these formulations is ....

C. S. Chekuri, A. V. Goldberg, D. R. Karger, M. S. Levine and C. Stein, "Experimental Study of Minimum Cut Algorithms", Oct 1996

....devoted to satisfiability, graph coloring, and clique problems and thus saw a large collection of results in this area. The ACM SIAM Symposium on Discrete Algorithms (SODA) has included a few such studies in each of its dozen events to date, such as the study of cut algorithms by Chekuri et al. CaDRKLS97] The Traveling Salesperson problem has seen large numbers of experimental studies (including the well publicized study of Jon Bentley [Ben90] made possible in part by the development of a library of test cases [Rei94] Graph coloring, whether in its NP hard version of chromatic number ....

C. S. Chekuri, A. V. Goldberg adn D. R. Karger, M. S. Levine, and C. Stein, Experimental study of minimum cut algorithms, Proc. 8th ACM/SIAM Symp. on Discrete Algs. SODA 97, SIAM Press, 1997, pp. 324--333.

....worst case performance for algorithms solving the minimum cut problem should not be the only guideline for the selection of an algorithm. There are numerous ways to combine the experimentally evaluated algorithms into hybrid versions, one of which is reported in [NOI94] and many others in [CGKLS96]. Except for NOIHY, we decided to refrain from trying more such experiments, because our only purpose here is to provide a (contemporary) basis for evaluating the practical performance of published minimum capacity cut algorithms. Our experimental experience makes us believe that the right ....

....a (contemporary) basis for evaluating the practical performance of published minimum capacity cut algorithms. Our experimental experience makes us believe that the right combination is highly dependent on structural properties of the considered class of instances. For the TSP type instances, [CGKLS96] is an excellent source of information, and we cannot identify other interesting classes that make the considerable experimental efforts that would have to be invested, appear worthwhile at the time of writing. Rather, we hope that interested readers with their particular instances will do the ....

C.S. Chekuri, A.V. Goldberg, D.R. Karger, M.S. Levine, and C. Stein (1996), "Experimental study of minimum cut algorithms", Report 96-132, NEC Research Institute, Inc. 25

....has led to a recent increase in the experimental study of algorithms. There have been a number of experimental studies of graph algorithms which focus on important problems such as shortest paths [13, 9] minimum spanning trees [21] network flow and matching [5, 8, 15, 23] and min cut algorithms [10]. These experiments provide valuable insight into the performance of different algorithms and can suggest new algorithmic choices. The authors of these studies reasonably spend most of their effort on the higher level algorithm details, so these papers have typically had a very limited discussion ....

C. Chekuri, A. Goldberg, D. Karger, M. Levine, and C. Stein, Experimental study of minimum cut algorithms. Technical Report 96-132, NEC Research Institute, Inc., October 1996.

....coloring, and clique problems and thus saw a large collection of results in this area. Proceedings of the ACM SIAM Symposium on Discrete Algorithms (SODA) have included a few such studies for each of the last few years; an outstanding recent example is the study of cut algorithms by Chekuri et al. [3]. The Traveling Salesperson problem has seen large numbers of experimental studies (including the well publicized study of Jon Bentley [2] made possible in part by the development of a library of test cases [23] Graph coloring, whether in its NP hard version of chromatic number determination or ....

Chekuri, C.S., Goldberg, A.V., Karger, D.R., Levine, M.S., and Stein, C., \Experimental study of minimum cut algorithms," Proc. 8th ACM/SIAM Symp. on Discrete Algs. (1997), 324-333.

....of having more edges inside the community than outside. Unfortunately, the most generic versions of balanced minimum cut graph partitioning are NP complete [14] On the other hand, if the constraint on the partition sizes is removed, then the problem lends itself to many polynomial time algorithms [15]; however, under this formulation, solutions will often be trivial cuts that leave one partition very small relative to the size of the original graph. Intuitively, balanced minimal cuts are hard because of the vast number of balanced partitions that one can place on a vertex set. Unrestricted ....

C. Chekuri, A. Goldberg, D. Karger, M. Levine, and C. Stein. Experimental study of minimum cut algorithms. In Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'97), pages 324-333, New Orleans, 1997.

....Karger and co workers have extended this paradigm to provide a series of algorithms with better and better running times and better success probabilities of returning a minimum cut. For details of these methods and an empirical evaluation of the different approaches to computing minimum cuts, see [3] and the references therein. 10.2 Gomory Hu Trees: Existence In this section, we look at two kinds of spanning trees of a capacitated undirected graph that capture the structure of minimum cuts in the graph. 10.2.1 Introduction Let G = V; E) be a connected undirected graph, and as before, let ....

C. Chekuri, A. Goldberg, D. Karger, M. Levine, and C. Stein, Experimental study of minimum cut algorithms, NECI TR 96-132 (October 1996). Available from http://www.neci.nj.nec.com/homepages/avg/webpub/webpub.html.

....a few. In this paper we compare experimentally the most important methods for the solution of the minimum cut problems on problem instances from the literature and on graphs originating from the solution of traveling salesman problems by branch and cut. Recently, a similar study has been published [4]. Whereas in [4] fast hybrid algorithms combining various minimum cut algorithms are presented, we compare in this paper the pure versions of the algorithms. For an undirected graph G = V; E) and W V we let ffi (W ) ffu; vg 2 E j u 2 W; v 2 V nWg denote the cut in G induced by W and write ....

....we compare experimentally the most important methods for the solution of the minimum cut problems on problem instances from the literature and on graphs originating from the solution of traveling salesman problems by branch and cut. Recently, a similar study has been published [4] Whereas in [4] fast hybrid algorithms combining various minimum cut algorithms are presented, we compare in this paper the pure versions of the algorithms. For an undirected graph G = V; E) and W V we let ffi (W ) ffu; vg 2 E j u 2 W; v 2 V nWg denote the cut in G induced by W and write ffi (v) instead ....

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C.S. Chekuri, A.V. Goldberg, D.R. Karger, M.S. Levine, and C. Stein. Experimental study of minimum cut algorithms. Technical Report 96-132, NEC Research Institute, Inc, 1996.

....exploit this duality. Nagamochi and Ibaraki [40] for instance, use edge contraction in their algorithm. Randomized edge contraction, introduced by Karger and Stein [32] leads to the fastest algorithm so far. An overview of these algorithms with a computational study is given by Chekuri et al. [17]. Interesting results have been obtained in determining polynomially solvable subclasses of generally NP hard problems. Robertson and Seymour [45] proved an old conjecture of Wagner: for each set of graphs that is closed under taking minors, there exists a finite set of graphs that are forbidden ....

C.S. Chekuri, A.V. Goldberg, D.R. Karger, M.S. Levine, C. Stein (1996). Experimental study of minimum cut algorithms, Technical report, NEC Research Institute, Princeton.

....has led to a recent increase in the experimental study of algorithms. There have been a number of experimental studies of graph algorithms which focus on important problems such as shortest paths [9, 5] minimum spanning trees [17] network flow and matching [1, 4, 10, 19] and min cut algorithms [6]. These experiments provide valuable insight into the performance of different algorithms and can suggest new algorithmic choices. The authors of these studies reasonably spend most of their effort on the higher level algorithm details, so these papers have typically had a very limited discussion ....

C. Chekuri, A. Goldberg, D. Karger, M. Levine, and C. Stein, Experimental study of minimum cut algorithms. Technical Report 96-132, NEC Research Institute, Inc., October 1996.

....3 0 2 3 0 2 4 4 3 7 7 7 5 : Iteration 1: S 0 = Z(S 0 ) 0; u(S 0 ) 0 0 0 0] p 1 (S 0 ) p 2 (S 0 ) p 3 (S 0 ) p 4 (S 0 ) p 5 (S 0 ) p 6 (S 0 ) 16 15 15 12 10 13 w(u(S 0 ) 0) 81) 81: S 1 : f1g; since p 1 (S 0 ) 0 is maximum. Iteration 2: S 1 = f1g; z(S 1 ) 16; u(S 1 ) [6 6 5 2]: p 2 (S 1 ) p 3 (S 1 ) p 4 (S 1 ) p 5 (S 1 ) p 6 (S 1 ) 2 1) Gamma 2 = 1 (2) Gamma 2 = 0 (1) Gamma 2 = Gamma1 (2) Gamma 3 = Gamma1 (2) Gamma 3 = Gamma1 w(u(S 1 ) 19) 1) 20: S 2 : f1; 2g; since p 2 (S 1 ) 0 is maximum. Iteration 3: S 2 = f1; 2g; z(S 2 ) 16 1 = 17; ....

....(S 1 ) p 3 (S 1 ) p 4 (S 1 ) p 5 (S 1 ) p 6 (S 1 ) 2 1) Gamma 2 = 1 (2) Gamma 2 = 0 (1) Gamma 2 = Gamma1 (2) Gamma 3 = Gamma1 (2) Gamma 3 = Gamma1 w(u(S 1 ) 19) 1) 20: S 2 : f1; 2g; since p 2 (S 1 ) 0 is maximum. Iteration 3: S 2 = f1; 2g; z(S 2 ) 16 1 = 17; u(S 2 ) [6 8 5 3]: p 3 (S 2 ) p 4 (S 2 ) p 5 (S 2 ) p 6 (S 2 ) 2) Gamma 2 = 0 (1) Gamma 2 = Gamma1 (1) Gamma 3 = Gamma2 (1) Gamma 3 = Gamma2 w(u(S 2 ) 22) 0) 22: stop, since p j (S 2 ) 0; 8j 2 JnS 2 : The greedy solution is S G = f1; 2g, with objective value Z G = 17. The dual greedy ....

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C. Chekuri, A. Goldberg, D. Karger, M. Levine, and C. Stein, Experimental study of minimum cut algorithms, NECI TR 96-132 (October 1996). Available from http://www.neci.nj.nec.com/homepages/avg/webpub/webpub.html

....of the minimum capacity cut algorithms we implemented for this study. The selection of these runs was influenced by experience with more than 100 000 runs that we performed while we prepared the final versions of the implementations and the experiments. Recently, a similar study has been published [CGKLS97]. Whereas in [CGKLS97] fast hybrid algorithms combining various minimum capacity cut algorithms are presented, we compare in this paper the pure versions of the algorithms. In particular, we do not propose any new algorithms. Rather, we have put a lot of effort in good implementations of ....

....cut algorithms we implemented for this study. The selection of these runs was influenced by experience with more than 100 000 runs that we performed while we prepared the final versions of the implementations and the experiments. Recently, a similar study has been published [CGKLS97] Whereas in [CGKLS97] fast hybrid algorithms combining various minimum capacity cut algorithms are presented, we compare in this paper the pure versions of the algorithms. In particular, we do not propose any new algorithms. Rather, we have put a lot of effort in good implementations of published algorithms in order ....

[Article contains additional citation context not shown here]

C.S. Chekuri, A.V. Goldberg, D.R. Karger, M.S. Levine, and C. Stein (1997), "Experimental study of minimum cut algorithms", in: Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'97), New Orleans, 324--333.

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C. Chekuri, A. V. Goldberg, D. Karger, M. Levine, and C. Stein. Experimental study of minimum cut algorithms. In Proc. of 8th SODA, 324--333, 1997.

....progress in understanding how to implement these algorithms, introduce new heuristics, and give an interesting set of problem generators. Note that this paper represents joint work with Chandra Chekuri, Andrew Goldberg, David Karger, and Clifford Stein. A preliminary version appeared in SODA 97 [8]. The paper is organized as follows. In Chapter 2 we review the theory behind the minimum cut algorithms, including definitions, characterizations of the problem, and descriptions of the algorithms. In Chapter 3 we discuss general implementation issues and details of each algorithm in turn. In ....

C. S. Chekuri, A. V. Goldberg, D. R. Karger, M. S. Levine, and C. Stein. Experimental Study of Minimum Cut Algorithms. In Proc. 8th ACM-SIAM Symposium on Discrete Algorithms, pages 324--333, 1997.

....progress in understanding how to implement these algorithms, introduce new heuristics, and give an interesting set of problem generators. Note that this paper represents joint work with Chandra Chekuri, Andrew Goldberg, David Karger, and Clifford Stein. A preliminary version appeared in SODA 97 [8]. The paper is organized as follows. In Chapter 2 we review the theory behind the minimum cut algorithms, including definitions, characterizations of the problem, and descriptions of the algorithms. In Chapter 3 we discuss general implementation issues and details of each algorithm in turn. In ....

C. S. Chekuri, A. V. Goldberg, D. R. Karger, M. S. Levine, and C. Stein. Experimental Study of Minimum Cut Algorithms. In Proc. 8th ACM-SIAM Symposium on Discrete Algorithms, pages 324--333, 1997.

....lines to a maximum flow code. Computational performance of algorithms for closely related problems, the maximum flow problem and the (global, e.g. over all s,t pairs) minimum cut problem has been studied extensively; see e.g. 1, 4, 5, 7, 18] for computational studies of the former problem and [3, 15, 16, 17, 19] for the latter. Both prob # Current address: InterTrust STAR Laboratory, 460 Oakmead Parkway, Sunnyvale, CA 94086. 1 We denote the number of vertices and edges in the input graph by n and m, respectively. lems can be solved well in practice: most problems that fit in RAM of a modern computer ....

....For our computations, we used a SUN Sparc Ultra 2 workstation with 256MB memory running SunOS 5.5.1. All the code is written in C and compiled with gcc and optimization option O4. Our implementations are written in the same style and are derived from the HaoOrlin algorithm implementation of [3]. We attempted to make all implementations as e#cient as possible. For our tests we use problem families from the previous minimum cut studies [3, 16, 17, 19] but instead of finding a minimum cut of a graph, we build a cut 2 A random choice is much less robust. tree. We omit the description of ....

[Article contains additional citation context not shown here]

C. S. Chekuri, A. V. Goldberg D. R. Karger, M. S. Levine, and C. Stein. Experimental Study of Minimum Cut Algorithms. In Proc. 8th ACM-SIAM Symposium on Discrete Algorithms, pages 324--333, 1997.

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Chandra C. Chekuri, Andrew V. Goldberg, David R. Karger, Matthew S. Levine, and Cliff Stein. Experimental study of minimum cut algorithms. To appear., January 1997.

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C. C. Chekuri, A. V. Goldberg, D. R. Karger, M. S. Levine, and C. Stein. Experimental study of minimum cut algorithms. In M. Saks, editor, Proceedings of the 8 th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 324--333. ACM-SIAM, January 1997.

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C. Chekuri, A. V. Goldberg, D. Karger, M. Levine, and C. Stein. Experimental study of minimum cut algorithms. In Proc. 8th ACM-SIAM SODA, 324--333, 1997.

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Chekuri, C., Goldberg, A., Karger, D., Levine, M. & Stein, C. "Experimental study of minimum cut algorithms," Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, 1997, p. 324-333.

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Chekuri, C., Goldberg, A. V., Karger, D. R., Levine, M. S., and Stein, C. "Experimental Study of Minimum Cut Algorithms". In Symposium on Discrete Algorithms (1997), pp. 324--333.

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C. Chekuri et al. Experimental Study of Minimum Cut Algorithms. In Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, 1997.

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Chekuri, C. S., A. V. Goldberg, D. R. Karger, M. S. Levine, C. Stein. 1997. Experimental study of minimum cut algorithms. Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms. ACM Press, New York, USA. 324-333. (The full version of the paper is available at www. cs. dartmouth. edu/~clif f/papers/MinCut Implement. ps. gz .)

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Chandra C. Chekuri, Andrew V. Goldberg, David R. Karger, Matthew S. Levine, and Cliff Stein. Experimental study of minimum cut algorithms. In Proceedings of the 8 th Annual ACM-SIAM Symposium on Discrete Algorithms [ACM97], pages 324--333.

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