D. Karger and S. Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows. In Proc. of the 27th Symp. on Theory of Computing, pages 18--25, 1995.  Home/Search   Document Details and Download   Summary   ACM   TOC   Related Articles   Check

....very special multipliers. These are exponential multipliers, which roughly stated arise in the Frank Wolfe scheme as the gradient of the potential function. The Shahrokhi Matula results catalyzed an intense and still active research e ort. See [LMPSTT91] GK94] GK95] LR98] PST91] R95] [KP95]. This research primarily showed how to better use an exponential potential function, still in the Frank Wolfe Lagrangian relaxation framework, to obtain faster algorithms for the minimum congestion problem, and generalizations. A logarithmic sliding barrier function, applied to the minimum ....

D. Karger and S. Plotkin, Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity ows, Proc. 27th Ann. ACM Symp. on Theory of Computing (1995) 18 - 25.

.... concentrated on the problem of minimizing the congestion of the edges (also called the concurrent ow problem) the algorithm was later extended for the minimum cost multi commodity problem, 32 in which the objective is to minimize a cost which depends on a cost function associated with the edges [18, 12, 8, 6]. The best approximation algorithms achieve a O( 2 knm) bound on the total running time 4 , so the multi commodity ow problem takes approximately as much time as k single commodity ow problems, ignoring polylog factors. The combinatorial approximation algorithms are all based on the same ....

D. Karger and S.A. Plotkin. Adding Multiple Cost Constraints to Combinatorial Optimization Problems with Applications to Multicommodity Flows. In Proc. 27th Symp. on Theory of Computing, pages 18-25, May 1995.

....very special multipliers. These are exponential multipliers, which roughly stated arise in the Frank Wolfe scheme as the gradient of the potential function. The Sharokhi Matula results catalyzed an intense and still active research e ort. See [LMPSTT91] GK94] GK95] LR98] PST91] R95] [KP95]. This research primarily showed how to better use an exponential potential function, still in the Frank Wolfe Lagrangian relaxation framework, to obtain faster algorithms for the minimum congestion problem, and generalizations. A logarithmic sliding barrier function, applied to the minimum ....

D. Karger and S. Plotkin, Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity ows, Proc. 27th Ann. ACM Symp. on Theory of Computing (1995) 18 - 25.

....that obtain comparable performance guarantees without solving the linear program. For instance, this is the case for packing and covering problems abstracting multicommodity flow problems (Klein et al. 1994; Goldberg, 1991; Radzik, 1995; Grigoriadis and Khachiyan, 1995; Plotkin et al. 1991; Karger and Plotkin, 1995). These algorithms are also faster than general linear programming for approximately solving fractional (relaxed) packing and covering problems. Such algorithms can be understood within the framework of probabilistic methods via a variant of randomized rounding called oblivious rounding, which ....

Karger, D. and Plotkin, S. (1995). Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows. In Proceedings of the Twenty-Seventh Annual ACM Symposium on Theory of Computing, pages 18--25, Las Vegas, Nevada.

....Therefore how to approximately solve these semidefinite relaxations efficiently, in both time and space, is practically important. All the previous work resorts to various general interior point methods [5, 113, 150] for this step. In the thesis we adapt the technique of Lagrangean relaxation [96, 105, 121, 87, 158] to cope with this crucial step. Specifically we use the framework of Plotkin, Shmoys, and Tardos [121] to obtain near optimal iv solutions to the semidefinite relaxations of MAXCUT and COLORING. Our results significantly reduce the work space required by the best known approximation algorithms ....

....they can handle instances that previous algorithms cannot even touch. The basis of our algorithms is the framework of Plotkin, Shmoys, and Tardos [121] which is related to the technique of Lagrangean relaxation. Lagrangean relaxation useful in exploiting the structure of mathematical programs [96, 105, 121, 87, 158]. It basically works as follows: Suppose we are given a set of constraints, over which an objective function is supposed to be optimized. Instead of solving it using general purpose algorithms such as ellipsoid methods [92, 68] or interior point methods [89, 147, 50] we could separate the ....

D. Karger and S. Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows. In ACM [2], pages 18--25.

....in the above sense, and moreover, are of similar nature to the algorithm CLS. See, for example, Grigoriadis and Khachiyan [17,18] and Villavicencio and Grigoriadis [39] who consider algorithms for block angular resource sharing problems, Plotkin, Shmoys, and Tardos [27] and Karger and Plotkin [20] who consider algorithms for fractional packing problems, and Bienstock [4,5] and Goldberg et al. 16] where results of computational experiments with these methods are discussed. Similar to algorithm CLS, each iteration of the algorithms above maintains an admissible point (i.e. a point that ....

D. Karger and S. Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity ows. Proceedings of the Twenty-Seventh Annual ACM Symposium on the Theory of Computing, pages 18-25, 1995.

....so that the residual capacity in the modi ed network is minimized. The problems studied here and in [2, 19] can be broadly classi ed as types of bicriteria problems. Recently, there has been substantial work on nding ecient approximation algorithms for a variety of bicriteria problems (see [13, 14, 17, 20 23] and the references therein) 5 Structure of an Optimal Solution T 2 T 1 (v 1 ; v 4 ) v 1 ; v 2 ) v 2 ; v 4 ) v 2 ; v 3 ) v 3 ; v 4 ) v 2 ; v 4 ) 5 10 15 4 5 14 15 22 32 Budget Fig. 2. Remaining weight of the trees T 1 and T 2 as a function of the budget. 7 In this section ....

D. Karger and S. Plotkin, Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity ows, in Proceedings of the 27th Annual ACM Symposium on the Theory of Computing (STOC'95), May 1995, pp. 18-25.

No context found.

David Karger and Serge Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows. In Symposium on the Theory of Computing, ACM Press, May 1995.

No context found.

David Karger and Serge Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows. In Symposium on the Theory of Computing, volume 27, pages 18--25. Association for Computing Machinery, ACM Press, May 1995.

....ow obeys arc capacity constraints and has minimum cost. Multicommodity ow problems can be expressed as linear programs, and most theoretical and practical algorithms use linear programming algorithms specialized for the problems structures. Combinatorial approximation algorithms in [GK95,KP95b,PST95] yield ows with costs slightly larger than the minimum cost and use capacities slightly larger than the given capacities. Theoretically, the running times of these algorithms are much less than that of linear programming based algorithms. We combine and modify the theoretical ideas in ....

....suce. More precisely, we say that a ow is optimal if it over ows the capacities by at most 1 factor and has cost that is within 1 of the optimum. Algorithms for computing approximate solutions to the multicommodity ow problem were developed in [LMP 95] no cost case) and [GK95,KP95b,PST95] minimum cost case) Theoretically, these algorithms are much faster than interior point method based algorithms for constant . The algorithm in [LMP 95] was implemented [LSS93] and was shown that indeed it often outperforms the more traditional approaches. Prior to our work, it was ....

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David Karger and Serge Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity ows. In Symposium on the Theory of Computing, volume 27, pages 18-25. Association for Computing Machinery, ACM Press, May 1995.

....parallelism in our algorithm, combined with locality of reference, will lead to efficient implementation on modern superscalar computers. Recently, after the publication of the preliminary version of this paper, Karger and Plotkin have discovered a new min cost multicommodity flow algorithm [8]. Their algorithm is based on capacity relaxation, and outperforms the algorithm described here in a sequential setting. Section 3 presents the continuous version of the algorithm and proves fast convergence assuming that at each iteration the algorithm computes an exact minimization of a ....

D. Karger and S. Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows. In Proc. 27th Annual ACM Symposium on Theory of Computing, May 1995.

....and scheduling algorithms assume a central scheduler that makes all the decisions. In Awerbuch and Azar [1994] the techniques of this paper were extended to the case where 1 See, for example, Shahrokhi and Matula [1990] Klein et al. 1994] Leighton et al. 1995] Plotkin et al. 1995] and Karger and Plotkin [1995]. 490 J. ASPNES et al. there are concurrent requests that have to be satisfied in a decentralized fashion. See Plotkin [1995] for a survey of different on line routing strategies. We note that another measure of performance for load balancing algorithms appears in Awerbuch et al. 1995] who ....

KARGER, D., AND PLOTKIN, S. 1995. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows. In Proceedings of the 27th Annual ACM Symposium on Theory of Computing (Las Vegas, Nev., May 29--June 1). ACM, New York, pp. 18 --25.

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D. Karger and S. Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows. In Proc. of the 27th Symp. on Theory of Computing, pages 18--25, 1995.

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D. Karger and S. Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows. In Proc. of the 27th Symp. on Theory of Computing, pages 18--25, 1995.

No context found.

D. Karger and S. Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity ows. In Proceedings of the 27th Annual ACM Symposium on Theory of Computing, pages 18-25, 1995.

No context found.

D. Karger and S. Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows. In Proc. of the 27th Ann. ACM Symp. on Theory of Computing, pages 18--25, 1995.

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D. Karger and S. Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows. In Proceedings of the 27th Annual ACM Symposium on Theory of Computing, pages 00--00, 1995.

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D. Karger and S. Plotkin, Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity ows, Proc. 27th Ann. ACM Symp. on Theory of Computing (1995) 18 - 25.

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S. Plotkin and D. Karger, Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows, In Proceedings of the 27th Annual ACM Symposium on Theory of Computing, (1995), 18-25.

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David Karger and Serge Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows. In Symposium on the Theory of Computing, volume 27, pages 18--25. Association for Computing Machinery, ACM Press, May 1995.

No context found.

D. Karger and S. Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows. In Proceedings, ACM Symposium on Theory of Computing, pages 18--25, 1995.

No context found.

David Karger and Serge Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows. In Symposium on the Theory of Computing, volume 27, pages 18--25. Association for Computing Machinery, ACM Press, May 1995.

No context found.

D. Karger and S. Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity ows. In Proceedings of 27th ACM STOC, pp. 18-25, 1995.

No context found.

D. Karger and S. A. Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity flows. In ACM Symposium on Theory of Computing, pages 18--25, 1995.

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D. Karger and S. Plotkin. Adding multiple cost constraints to combinatorial optimization problems, with applications to multicommodity ows. In Proc. of the 27th Ann. ACM Symp. on Theory of Computing, pages 18-25, 1995.

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