G. Even, J. Naor, S. Rao, and B. Schieber. Fast approximate graph partitioning algorithms. SIAM Journal on Computing, 28:2187-2214, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... of cost O(b log n) Leighton and Rao [LR88, LR99] show how an algorithm that nds a approximate minratio cut can be used to nd a 2 3 balanced cut of cost O(b ) the approximation ratio = O(log n) that they achieve is the best currently known, see also [Shm97] Even, Naor, Rao and Schieber [ENRS97] devise a di erent algorithm that also nds a 2 3 balanced cut of cost O(b log n) We show below that amortized cuts can be used to obtain also bicriteria approximation algorithms (in addition to approximation algorithms) for minimum bisection. In fact, our algorithm is similar to the one of ....

G. Even, J. Naor, S. Rao, and B. Schieber. Fast approximate graph partitioning algorithms. In Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 639-648. ACM, New York, 1997.

....cut (i.e. a cut that partitions the vertices into two sets, each of cardinality at most 2n=3) whose cost is at most O(log n) times that of the minimum cost bisection. The techniques and results of Leighton and Rao found many applications and inspired additional work, see e.g. LR99, Shm97, ENRS99] However, prior to our work there was no major progress on the approximation ratio of minimum bisection (i.e. when the strict constraint on the cardinalities of two sides of the cut cannot be relaxed) On the one hand, there is no hardness of approximation result that excludes the possibility ....

.... We devise an algorithm that approximates the minimum bisection within a ratio of O(log 2 n) This approximation ratio improves over the previous (linear in n) approximation ratio significantly, and is, in particular, in the same ballpark as the bicriteria algorithms of [LR88, LR99] and [ENRS99] Our algorithm extends (with the same approximation ratio) to minimum bisection in graphs with arbitrary nonnegative edge costs and polynomially bounded nonnegative integer vertex weights. It also extends to cutting away from the graph k vertices, where k is given as part of the input, and to ....

G. Even, J. Naor, S. Rao, and B. Schieber. Fast approximate graph partitioning algorithms. SIAM J. Comput., 28(6):2187--2214, 1999.

.... of cost O(b log n) Leighton and Rao [LR88, LR99] show how an algorithm that finds a approximate minratio cut can be used to find a 2 3 balanced cut of cost O(b ) the approximation ratio = O(log n) that they achieve is the best currently known, see also [Shm97] Even, Naor, Rao and Schieber [ENRS97] devise a different algorithm that also finds a 2 3 balanced cut of cost O(b log n) We show below that amortized cuts can be used to obtain also bicriteria approximation algorithms (in addition to approximation algorithms) for minimum bisection. In fact, our algorithm is similar to the one of ....

G. Even, J. Naor, S. Rao, and B. Schieber. Fast approximate graph partitioning algorithms. In Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 639--648. ACM, New York, 1997.

....some factor times the optimal partitioning. The worst case ratio between the cost of the computed solution and the cost of the optimal solution is called the approximation factor. Leighton and Rao [LR88] presented an approximation algorithm with an approximation factor of O(log n) Even et al. [ENRS97] presented an approximation algorithm that deals with graph partitioning into more than two parts with the same approximation factor. Experiments in implementing these algorithms seem to indicate that the actual quality of the computed partitions are much better than what the worst case analysis ....

G. Even, J. Naor, S. Rao, and B. Schieber, \Fast approximate graph partitioning algorithms ", Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, 1997, pp. 639-648.

....Instead, they incorporate the size constraints implicitly in the objective function. This paper presents a new network flow approach for partitioning circuits into tree hierarchies. We formulate a linear program for the hierarchical tree partitioning problem by spreading metrics proposed in [3][4]. The size constraints in partitioning can be formulated directly as linear constraints. Motivated by the duality between the linear programs for partitioning and network flow problems, we devise a heuristic algorithm based on network flow and spreading metric computations. Experimental results ....

....to solve them. In this paper, we propose a constructive algorithm for HTP based on a new network flow approach. First, we derive a linear programming formulation for the HTP problem by spreading metrics (length functions on the graph edges) proposed by Even et al. for graph partitioning [3][4]. Informally, a spreading metric is an assignment of fractional lengths on graph edges so that heavy subgraphs (subgraphs with large total node size) will have a large enough radius, i.e. the subgraphs are spread apart in the associated metric space. Using spreading metrics, the size constraints ....

[Article contains additional citation context not shown here]

G. Even, J. Naor, S. Rao, and B. Schieber, "Fast approximate graph partitioning algorithms," submitted to Symposium of Discrete Algorithms, 1997.

....of the vertices of a graph into two sets each containing at least one third of the vertices; its weight is the total weight of edges connecting the two sets. There is an algorithm to find a 1 3 balanced cut whose weight is O(log n) times the minimum weight of a bisector (Leighton and Rao, 1988; Even et al. 1997). Note that this algorithm is not, strictly speaking, an approximation algorithm for any one optimization problem: the output of the algorithm is a solution to one problem while the quality of the output is measured against the optimal value for another. Nevertheless, the algorithm is nearly as ....

Even, G., Naor, J. S., Rao, S., and Schieber, B. (1997). Fast approximate graph partitioning algorithms. In Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 639--648, New Orleans, Louisiana.

....backedges B whose removal from G will give us a DAG and the sum of whose weights is minimum. If we assign a weight of one to each edge, then this is the feedback arc set problem which is NP hard [GJ79] Several approximation algorithms have been proposed for the weighted version of this problem [ENRS97, LMT90, ST97] Any of these can be used to compute G dag if the number of nodes in G is large. 5 Experimental Results In order to evaluate the performance of our algorithms and to explore the dependency of our algorithms on values in the parameter space, we implemented a simpler variant of the ....

Guy Even, Joseph (Seffi) Naor, Satish Rao, and Baruch Schieber. Fast approximate graph partitioning algorithms. In Proceedings of the 8th ACM-SIAM Symposium on Discrete Algorithms, New Orleans, Louisiana, 1997.

....backedges B whose removal from G will give us a DAG and the sum of whose weights is minimum. If we assign a weight of one to each edge, then this is the feedback arc set problem which is NP hard [GJ79] Several approximation algorithms have been proposed for the weighted version of this problem [ENRS97, LMT90, ST97]. Any of these can be used to compute G dag if the number of nodes in G is large. 5 Experimental Results In order to evaluate the performance of our algorithms and to explore the dependency of our algorithms on values in the parameter space, we implemented a simpler variant of the BackEdge ....

Guy Even, Joseph (Seffi) Naor, Satish Rao, and Baruch Schieber. Fast approximate graph partitioning algorithms. In Proceedings of the 8th ACM-SIAM Symposium on Discrete Algorithms, New Orleans, Louisiana, 1997.

....and Rao [11] and Shmoys [15] So far, the best result for (GBP) in the literature is due to Leighton and Rao [10] They show that there exists a polynomial algorithm for nding a b balanced cut with b = 1 3 of value O(logn) w , where w is the minimal value of the (GBP) Even et.al. [3] get the similar result by using an alternative approach. Note that these are not true approximation algorithms for (GBP) 17] since b 6= 1 2 . For the planar graph, there exists a 2 approximation algorithm due to Garg et.al. 7] Many heuristic methods have been proposed in the literature. In a ....

G. Even, J. Naor, S. Rao and B. Schieber, \Fast approximate graph partitioning algorithms," in 8th SODA, (1997) pp. 639-648.

....and Rao [11] and Shmoys [15] So far, the best result for (GBP) in the literature is due to Leighton and Rao [10] They show that there exists a polynomial algorithm for nding a b balanced cut with b = 1 3 of value O(logn) w , where w is the minimal value of the (GBP) Even et.al. [3] get the similar result by using an alternative approach. Note that these are not true approximation algorithms for (GBP) 17] For the planar graph, there exists a 2 approximation algorithm due to Garg et.al. 7] Many heuristic methods have been proposed in the literature. In a recent note [2] ....

G. Even, J. Naor, S. Rao and B. Schieber, \Fast approximate graph partitioning algorithms," in 8th SODA, (1997) pp. 639-648.

....implies that D(i) D(0) ffl i X j=1 (f j Gamma f j Gamma1 )ff(j Gamma 1) 1) Problem Previous Best Our running time Improvement Max. multicomm. O( Gamma3 m 2 log m) 14] mC 1 kT sp Gamma1 flow Fractional Packing [5] mC 1 T orc Spreading metrics O( Gamma3 nm log nT sp ) [3] mC 1 (nT sp ) Gamma1 Maximum O(k( Gamma2 log k) log nT mcf ) 2k log k)C 2 T mcf In constants concurrent flow [12, 10] 2k log k m)C 2 T sp For k m=n Max. cost bounded O(k( Gamma2 log k) log n log( Gamma1 k) 2k log k 1)C 2 T mcf log( Gamma1 k) concurrent flow T mcf ....

....(l) f(S) where dist r;v (l) is the distance from r to v under the length function l and f( is a function only of the size of S. For the linear arrangement problem f(S) jSj Gamma 1) jSj Gamma 3) 4 [2] while for the problem of computing a ae separator 1 f(S) is defined as jSj Gamma aejV j [3]. Since the length function l is positive, the shortest paths from r to the other vertices in S forms a tree the shortest path tree rooted at r. Thus the above constraints can be equivalently stated as: for any tree T , for any subset S of vertices in T and for any vertex r 2 S X v2S dist ....

G. Even, J. Naor, S. Rao, and B. Schieber. Fast approximate graph partitioning algorithms. In Proceedings, ACM-SIAM Symposium on Discrete Algorithms, pages 639--648, 1997.

No context found.

G. Even, J. Naor, S. Rao, and B. Schieber, \Fast approximate graph partitioning algorithms", SIAM Journal on Computing. Volume 28, Number 6, pp. 2187-2214, 1999.

No context found.

G. Even, J. Naor, S. Rao, and B. Schieber, "Fast approximate graph partitioning algorithms", SIAM Journal on Computing. Volume 28, Number 6, pp. 2187-2214, 1999.

....the sizes of the optimal b balanced cuts of V and U are bounded by p MDS(G) Therefore, the proof of Lemma 5 can be made constructive based on approximate b balanced cuts. Another way to compute simultaneous separators with relaxed balance parameters uses the spreading metric based algorithm [ENRS99] for simultaneous separators. One application of this algorithm computes a simultaneous separator (S; V S) of size cS p MDS(G) log n (for some constant cS ) with the following relaxed balance parameters: 1. minfjSj; jV Sjg 1 8 jV j; and 2. minfw(S) w(V S)g 1 6 w(V ) Weight ....

G. Even, J. Naor, S. Rao and B. Schieber, \Fast approximate graph partitioning algorithms", SIAM J. on Computing, 28(6):2187-2214, 1999.

No context found.

G. Even, J. Naor, S. Rao, and B. Schieber. Fast approximate graph partitioning algorithms. SIAM Journal on Computing, 28:2187-2214, 1999.

No context found.

G. Even, J. Naor, S. Rao, and B. Schieber. Fast approximate graph partitioning algorithms. SIAM Journal on Computing, 28:2187--2214, 1999.

No context found.

G. Even, J. Naor, S. Rao, and B. Schieber. Fast approximate graph partitioning algorithms. In Proceedings, ACM-SIAM Symposium on Discrete Algorithms, pages 639--648, 1997.

No context found.

G. Even, J. S. Naor, S. Rao and B. Schieber, Fast approximate graph partitioning algorithms, SIAM Journal on Computing, 6 (1999), 2187-2214.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC