V. Bafna, P. Berman, and T. Fujito. Constant ratio approximations of the weighted feedback vertex set problem. In Proceedings of the 6th International Symposium on Algorithms and Computation (ISAAC'95), pages 142--151, 1995. LNCS 1004.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....sizes of jG i j; i = 1 : t are all equal. A constant approximation algorithm that works also when the sizes of jG i j; i = 1 : t are not necessarily equal is described in [3] A better algorithm, which achieves an error constant of 2, is given in [4] A similar algorithm is also given in [1]. The cited error constants are determined by a worst case analysis; in practice these algorithms usually find closer to optimal solutions, especially when there are few loops. We use the simplest greedy algorithm analyzed in [4] as part of our hybrid loop breaking algorithm. 4 Methods Our loop ....

Bafna V., Berman P., and Fujito T., Constant ratio approximations of the weighted feedback vertex set problem for undirected graphs, Proc. Sixth Annual Symposium on Algorithms and Computation (ISAAC 95) . 13

....performed very badly when presented with an appropriate example. Becker and Geiger offered an algorithm that finds a loop cutset for which the logarithm of the state space is guaranteed to be a constant factor off the optimal value [BG94, BG96] Bafna et al. and Fujito developed similar algorithms [BBF95, Fu96]. While the approximation algorithms for the loop cutset problem are quite useful, it is worthwhile to invest in finding a minimum loop cutset, rather than an approximation, because the cost of finding such a loop cutset is amortized over the many iterations of the conditioning method. In fact, ....

Bafna V., Berman P., and Fujito T., Constant ratio approximations of the weighted feedback vertex set problem for undirected graphs, Proceedings Sixth Annual Symposium on Algorithms and Computation (ISAAC95), 142--151.

....i = 1 : t are all equal. A constant approximation algorithm that works also when the sizes of jG i j; i = 1 : t are not necessarily equal is described in [22] A full analysis of this algorithm, which achieves an error constant of 2, is given in [23] A similar algorithm is also given in [24]. The cited error constants are determined by a worst case analysis; in practice these algorithms usually find closer to optimal solutions, especially when there are few loops. We use the simplest greedy algorithm analyzed in [23] as part of our hybrid loop breaking algorithm. 4 Methods Our loop ....

Bafna V., Berman P., and Fujito T., Constant ratio approximations of the weighted feedback vertex set problem for undirected graphs, Proc. Sixth Annual International Symposium on Algorithms and Computation (ISAAC 95) . Lecture Notes in Computer Science, volume 1004. , Springer-Verlag, Berlin, 1995, 142--151.

....by a simple but non standard form of the integer program using matroid rank functions. A primal dual approximation algorithm for such ND( s is then designed based on this formulation and the dual of its linear programming relaxation, which is simpler than those algorithms for FVS given in [BBF95, BG94, CGHW96] In particular our algorithm does not look into nor modify explicitly, unlike the previous algorithms for FVS, any special structure in graphs under consideration. An analysis of this algorithm reveals that its performance ratio can be reduced to the combinatorial bound arising ....

....hereditary . Such a bound for VC has been continuously improved in the last few years, and currently it is known to be as large as 7 6 [Has97] The approximation ratio of [BGNR94] for the unweighted FVS was subsequently extended to the one for the weighted FVS and was further improved to 2 in [BBF95, BG94] matching the best constant factor known for VC. Recently Chudak et al. CGHW96] gave a primal dual interpretation of these 2 approximation algorithms of [BBF95, BG94] They also provided a new primal dual algorithm for FVS, which has the same performance ratio but is slightly simpler ....

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V. Bafna, P. Berman, and T. Fujito. Constant ratio approximations of the weighted feedback vertex set problem for undirected graphs. In ISAAC '95, pages 142--151, 1995.

....off the optimal value. An adaptation of these approximation algorithms has been included in version 4. 0 of FASTLINK, a popular software for analyzing large pedigrees with small number of genetic markers (Becker et al. 1998) Similar algorithms in the context of undirected graphs are described by Bafna, Berman, and Fujito (1995) and Fujito (1996) While approximation algorithms for the loop cutset problem are quite useful, it is still worthwhile to invest in finding a minimum loop cutset rather than an approximation because the cost of finding such a loop cutset is amortized over the many iterations of the conditioning ....

Bafna, V., Berman, P., & Fujito, T. (1995). Constant ratio approximations of the weighted feedbackvertex set problem for undirected graphs. In Proceedings of the Sixth Annual Symposium on Algorithms and Computation (ISAAC95), pp. 142--151.

....weight a i and removing them from H i . These steps are iterated until the reduced graph H i becomes a forest. For the feedback vertex set problem in general undirected graphs, two slightly different 2 approximation algorithms are described in Becker and Geiger [3] and by Bafna, Berman, and Fujito [1]. These algorithms improve the approximation algorithms of Bar Yeruda et al. 2] who also give a reduction procedure from the loop cutset problem to the minimum weighted feedback vertex set problem. The proposed algorithms also can find a loop cutset which, under specific conditions explained in ....

.... E G times at a constant amortized cost each. Moreover, the complexity of the second phase does not increase the total complexity of the algorithm. In [18] Chudak, Goemans, Hochbaum, and Williamson showed how the algorithms due to Becker and Geiger [3] and Bafna, Berman, and Fujito [1] can be explained in terms of the primal dual method for approximation algorithms that are used to obtain approximation algorithms for network design problems. The primal dual method starts with an integer programming formulation of the problem under consideration. It then simultaneously builds a ....

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V. Bafna, P. Berman, and T. Fujito, Constant ratio approximations of the weighted feedback vertex set problem for undirected graphs, in ISAAC95, Algorithms and Computation, J. Staples, P. Eades, N. Katoh and A. Moffat Eds., Lecture Notes in Computer Science Vol.1004, Springer-Verlag (1995) pp. 142-151.

....and in this sense it is not a combinatorial algorithm. The algorithm and its analysis are quite elaborate, and they are overviewed in Section 3. This result almost matches the 2 approximation algorithms known for the vertex multiway cut problem [GVY94] and for the feedback vertex problem [BG94, BBF95]. The subset feedback set problem belongs to the class of covering problems, and as such can be cast as a linear program whose dual is a packing problem, which can also be interpreted as a (standard) flow problem. However, the integrality gap of this linear program can be as large as ....

....a set of inter saturated vertices. Clearly, the weight of the intra saturated vertices in the cut can be at most the sum of the demands. Thus, we get that there exists a cut whose weight is at most twice the sum of the demands. The feedback vertex set problem can be approximated by a factor of 2 [BG94, BBF95] using local techniques, which bear similarity to the techniques used for approximating the vertex cover problem. We are quite doubtful whether such techniques can be used for the subset feedback set problem since finding an approximate fs; tg minimum cut is a special case of the subset feedback ....

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V. Bafna, P. Berman and T. Fujito, "Constant ratio approximations for the weighted feedback vertex set problem for undirected graphs", 6th Annual International Symposim on Algorithms and Computation (ISAAC), pp. 142-151, 1995.

....constructed such that it contains as many high degree vertices as possible. Remark In a preliminary version of this paper, presented in [BaGNR94] we conjectured that a constant performance ratio is attainable by a polynomial time algorithm for the WFVS problem. This has been recently verified in [BeG94, BaBF94] where a performance ratio of 2 has been obtained. Acknowledgment We would like to thank David Johnson for bringing [EP62] to our attention, and Samir Khuller for helpful discussions. ....

Bafna V., Berman P., and Fujito T., Constant ratio approximations of the weighted feedback vertex set problem for undirected graphs, to appear in Proceedings of ISAAC 96.

....algorithm and analysis here are an application of the algorithm and theorem given in the survey. We now review previously known work. For FVS in general undirected graphs, two slightly different 2 approximation algorithms were given recently by Becker and Geiger [6] and Bafna, Berman, and Fujito [4]; see Chudak et al. for an overview [8] These algorithms improve on a log n approximation algorithm of Bar Yehuda, Geiger, Naor, and Roth [5] where n is the number of vertices. They also gave a 10 approximation algorithm for the case of undirected planar graphs, which we can show to be a ....

V. Bafna, P. Berman, and T. Fujito. Constant ratio approximation of the weighted feedback vertex set problem for undirected graphs. In J. Staples, P. Eades, N. Katoh, and A. Moffat, editors, ISAAC '95 Algorithms and Computation, number 1004 in Lecture Notes in Computer Science, pages 142--151, 1995.

....Two 2 Approximation Algorithms for the Feedback Vertex Set Problem in Undirected Graphs Fabi an A. Chudak Cornell University Michel X. Goemans y M.I.T. Dorit S. Hochbaum z U.C. Berkeley David P. Williamson x IBM Watson Abstract Recently, Becker and Geiger [3] and Bafna, Berman, and Fujito [1] gave 2 approximation algorithms for the feedback vertex set problem in undirected graphs. We show how their algorithms can be explained in terms of the primal dual method for approximation algorithms, which has been used to derive approximation algorithms for network design problems [7] In the ....

....of the algorithm. The first non trivial approximation algorithm was given by Bar Yehuda, Geiger, Naor, and Roth [2] and has a performance guarantee of log n, where n is the number of vertices. Recently, two slightly different 2 approximation algorithms were given by Bafna, Berman, and Fujito [1] and Becker and Geiger [3] The goal of this note is to present the two 2 approximation algorithms in terms of the primaldual method for approximation algorithms. This method has been very successful in deriving approximation algorithms for network design problems (see Goemans and Williamson [7] ....

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V. Bafna, P. Berman, and T. Fujito. Constant ratio approximation of the weighted feedback vertex set problem for undirected graphs. In J. Staples, P. Eades, N. Katoh, and A. Moffat, editors, ISAAC '95 Algorithms and Computation, number 1004 in Lecture Notes in Computer Science, pages 142--151. Springer-Verlag, 1995.

....and any minimally feasible solution in a graph G with weights on its nodes assigned according to wG . The local ratio theorem of Bar Yehuda and Even and its generalization were used as a key approximation principle in approximation of the VC problem [BE85] and the feedback vertex set problem [BBF95] respectively. In fact it is applicable to a node deletion problems for any hereditary property, and so it is presented below in more general form. A family of nonnegative weight functions fw i : V Q ; i = 1; 1 1 1 ; kg is called a decomposition of a nonnegative weight function w : V Q ....

.... problem for such a matroidal property is usually referred to as the feedback vertex set (FVS) problem, whose NP completeness appeared already in the Karp s original list [Kar72] The best performance ratio for this problems is currently a constant of 2, obtained first by Bafna et al. BBF95] and, independently, by Becker and Geiger [BG94] Our work is motivated by the approach presented in the former one, and for this problem LocalRatio ; w is similar to their algorithm in [BBF95] they used, however, such a weight function that wG (u) d(u) 0 1, not rank proportional, and as ....

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V. Bafna, P. Berman, and T. Fujito. Constant ratio approximations of the weighted feedback vertex set problem for undirected graphs. In ISAAC '95 Algorithms and Computation, volume 1004 of Lecture Notes in Computer Science, pages 142--151, 1995.

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V. Bafna, P. Berman, and T. Fujito. Constant ratio approximations of the weighted feedback vertex set problem. In Proceedings of the 6th International Symposium on Algorithms and Computation (ISAAC'95), pages 142--151, 1995. LNCS 1004.

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V. Bafna, P. Berman, and T. Fujito. Constant ratio approximation of the weighted feedback vertex set problem for undirected graphs. In J. Staples, P. Eades, N. Katoh, and A. Moffat, editors, ISAAC '95 Algorithms and Computation, number 1004 in Lecture Notes in Computer Science, pages 142--151. Springer-Verlag, 1995. 11

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V. Bafna, P. Berman, and T. Fujito. Constant ratio approximation of the weighted feedback vertex set problem for undirected graphs. In J. Staples, P. Eades, N. Katoh, and A. Moffat, editors, ISAAC '95 Algorithms and Computation, number 1004 in Lecture Notes in Computer Science, pages 142--151, 1995.

No context found.

V. Bafna, P. Berman, and T. Fujito. Constant ratio approximations of the weighted feedback vertex set problem. In Proceedings of the 6th International Symposium on Algorithms and Computation (ISAAC'95), pages 142--151, 1995. LNCS 1004.

No context found.

V. Bafna, P. Berman, and T. Fujito. Constant ratio approximations of the weighted feedback vertex set problem. In Proceedings of the 6th International Symposium on Algorithms and Computation (ISAAC'95), pages 142--151, 1995. LNCS 1004.

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