J.-H. Lin and J. S. Vitter. #-approximations with minimum packing constraint violation. In Proceedings of the ACM Symposium on Theory of Computing, pages 771--782, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(for the greedy algorithm [2] 3.16 [3] 2.41 [4] and more recently 1.74 [5] The # median problem is harder to approximate due to the restriction on the number of servers (#) however, there are approximations with an extra relaxation on that restriction. For general graphs, Lin and Vitter [6] approximated the cost within a factor of ##### of optimal by relaxing the restriction of the number of servers to be up to ## # #### # ####. Arora, Raghavan, and Rao [7] extended the techniques of Lin and Vitter to achieve a polynomial time approximation for the Euclidean space. 0 1 3 2 ....

....variables which are used in the original # median problem. In the worst case, this is only a factor of # more variables. Thus, results obtained for the # median problem are also valid for our problem with proper adjustment. Specifically, we can use the # approximation suggested by Lin and Vitter [6] which finds locations at the cost not more than ## # ## of the optimal cost, but it might need a fac 5 torofupto## # # #### # ###more service centers. This is most likely the best one can hope to achieve for the # median problem if an # approximation is desired for the cost [7] It is ....

[Article contains additional citation context not shown here]

Jyh-Han Lin and Jeffrey Scott Vitter, "#-approximations with minimum packing constraint violation," in STOC'92, Victoria, B.C., Canada, 1992.

....of which needs time O(n ) time. Thus, the total running time is O(log(nC)n ) which is bounded by a polynomial in the input size and 1= 7 Approximation Algorithm on General Graphs In this section we use a linear programming relaxation in conjunction with filtering techniques (cf. [19]) to design an approximation algorithm. The algorithm and its analysis are very similar to those given in [25] for the Traveling Purchaser Problem. The basic outline of our algorithm is as follows: 1. Formulate BCCMED as an integer linear program (IP) 2. Solve the linear programming ....

J. H. Lin and J. S. Vitter. "-approximations with minimum packing constraint violation. In Proceedings of the 24th Annual ACM Symposium on the Theory of Computing, pages 771--781, 1992.

....the work of Charikar and Guha [5] which establishes a slightly lower approximation ratio of 1.728. The first constantfactor approximation for the k median problem was given by Charikar et al. 6] and is also LP based. That work follows a sequence of bicriteria results utilizing LPbased techniques [30, 31]. These bicriteria results produce a configuration of size O(k) with cost at most a constant factor times that of an optimal configuration of size k. Jain and Vazirani [22] give the first nearly linear time (in the input size) combinatorial algorithms for the facility location and k median ....

J.-H. Lin and J. S. Vitter. #-approximations with minimum packing constraint violation. In Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 771--782, May 1992.

....for the MES problem. III. Algorithms for Single Egress Variant The SES problem can be shown to be a version of the generalized assignment problem (GAP) which is known to be NP hard and has been well studied in the operations research and theoretical computer science communities. See for example, [13] and [14] The definition of GAP is as follows. Generalized Assignment Problem: Given # jobs and # machines, a processing time p rs and cost c rs for processing job r on machine s, and a total processing time T s available for each machine s, compute an assignment f : 1, # # 1, # of ....

J.-H. Lin and J. S. Vitter, "#-approximations with minimum packing constraint violation," in Proceedings of the 24th Annual ACM Symposium on the Theory of Computation, Victoria, Canada, May 1992, pp. 771-- 782.

.... algorithms have been proposed for this problem using a variety of techniques (see [23] for a survey) The rst constant factor approximation algorithm for this problem was given by Shmoys, Tardos, and Aardal [24] and was based on LP rounding and a ltering technique due to Lin and Vitter [18]. Later, the factor was improved by Chudak and Shmoys [3, 4] to 1 2=e. Jain and Vazirani [13] gave a primal dual algorithm for this problem, achieving a factor of 3. Strategies based on local search and greedy improvement for facility location problems have also been studied. The work of ....

J.H. Lin and J.S. Vitter, -approximations with minimum packing constraint violation, In Proceedings of the 24th ACM Symposium on Theory of Computing 1992, 771-782.

....show how to combine coloring techniques from [16] with our approach in order to encompass the assignment of frequencies. Related Problems: Uncapacitated facility location is MAX SNP hard [7] and has several constant factor approximations, using local search [1, 4, 13] linear program rounding [15, 22] and primal dual approach [10] to mention a few. In addition, there has been work on capacitated facility location, where either the capacities are hard [6, 13, 19] or where we are allowed multiple copies of a facility at a location [5, 10] Facility location variants arise in numerous ....

....gap otherwise (the proofs of this fact are omitted, but follow easily from previous work [22] In essence, we show that it is not hard to incorporate the interference and coloring constraints into any rounding scheme that preserves locality. Classical facility location rounding schemes [15, 22] do preserve this property. In view of the numerous applications mentioned above, we feel that understanding the power of these rounding techniques under additional constraints is of independent interest. In the next section, we present the various models and the approximation ratios we obtain ....

J.-H. Lin and J. S. Vitter. -approximations with minimum packing constraint violations. Proceedings of 24th ACM STOC, 1992.

....consider the asymmetric versions of these problems, where we still require the triangle inequality, but allow the possibility that c ij #= c ji . The asymmetric versions of UFL and k median are intimately tied to the set cover problem. The best algorithms known for these two clustering problems [4, 7] are based on the greedy set cover algorithm [2, 6, 8] yielding approximation algorithms with O(log N) performance guarantees (though for k median this is only a bicriterion approximation) This note shows, by a simple reduction from set cover, that these factors are the best possible, up to a ....

....known, which is not surprising in light of our hardness results below. However, one can consider a bicriterion (#, #) approximation algorithm, which returns a solution F with #k such that cost( F ) #OPT , where OPT is the optimal cost attainable using only k centers. Lin and Vitter [7] gave a bicriterion ( 1 ) 1 ln N) 1 #) approximation, where # 0 can be chosen arbitrarily. Again, this algorithm makes no assumption on the distance function. They also provide some hardness results for k median, but our results are much stronger. 2 Hardness of approximation The ....

J.-H. Lin and J. S. Vitter, "#-approximations with minimum packing constraint violation", Proc. 24th Annual ACM Symp. on Theory of Computing, (1992) 771-782.

.... O( as Weighted Fair Queueing [22, 23] Early papers on EDF include Ferrari and Verma [11] and Verma, Zhang and Ferrari [27] For an overview of different scheduling schemes see [15, 30] Our algorithm for choosing session routes combines the path filtering technique of Lin and Vitter [19] with a rounding scheme of Karp, Leighton, Rivest, Thompson, Vazirani and Vazirani [14] This approach was first used by Srinivasan and Teo [26] in the context of static routing. An alternative approach is to assume that the packet arrivals are generated by stochastic processes. Each packet is ....

....the sum of the congestion and the dilation up a constant factor. In conjunction with the scheduling results of [16, 17] this provides a constant factor approximation for minimizing the routing time. Srinivasan and Teo constructed their routes using the path filtering technique of Lin and Vitter [19] coupled with a rounding technique for column sparse matrices due to Karp, Leighton, Rivest, Thompson, Vazirani and Vazirani [14] In this section, we study the following problem. We are given a set of sessions, each of which is specified by its burst size oe i , its rate ae i , its source and ....

J. Lin and J. S. Vitter. "-Approximations with minimum packing constraint violation. In Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 771 -- 782, Victoria, B.C. Canada, May 1992.

....and Guha [2] which establishes a slightly lower approximation ratio of 1:728. The first constant factor approximation for the k median problem was recently given by 1 Charikar et al. 3] and is also LP based. That work follows a sequence of bicriteria results utilizing LPbased techniques [14, 15]. Jain and Vazirani [10] give the first nearly linear time combinatorial algorithms for the facility location and k median problems, achieving approximation ratios of 3 and 6, respectively. While the latter algorithms are combinatorial, the primal dual approach used in their analysis is based on ....

J.-H. Lin and J. S. Vitter. "-approximations with minimum packing constraint violation. In Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 771--782, May 1992.

....the greedy algorithm [14] 3.16 [22] 2.41 [13] and more recently 1.74 [9] The median problem is harder to approximate due to the restriction on the number of servers ( however, there are approximations with an extra relaxation on that restriction. For general graphs, Lin and Vitter [20] approximated the cost within a factor of of optimal by relaxing the restriction of the number of servers to be up to 4560 . Arora, Raghavan, and Rao [4] extended the techniques of Lin and Vitter to achieve a polynomial time approximation for the Euclidean space. To show ....

....which are used in the original median problem. In the worst case, this is only a factor of more variables. Thus, results obtained for the median problem are also valid for our problem with proper adjustment. Specifically, we can use the approximation suggested by Lin and Vitter [20] which finds locations at the cost not more than k of the optimal cost, but it might need a factor of up to 52260 more service centers. This is most likely the best one can hope to achieve for the median problem if an approximation is desired for the cost [4] It is ....

[Article contains additional citation context not shown here]

J.-H. Lin and J. S. Vitter. -approximations with minimum packing constraint violation. In STOC'92, Victoria, B.C., Canada, 1992.

....that the greedy algorithm is an O(log n) approximation algorithm for this problem, and provided instances to verify that this analysis is asymptotically tight. In fact, this result was shown for the more general setting, in which the input points need not belong to a metric space. Lin Vitter [12] gave an elegant technique, called filtering, for rounding fractional solutions to linear programming relaxations. As one application of this technique for designing approximation algorithms, they gave another O(log n) approximation algorithm for the uncapacitated facility location problem. ....

J.-H. Lin and J. S. Vitter. #-approximations with minimum packing constraint violation. In Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 771--782, 1992.

....location, and we can obtain a solution in which the number of copies of p we open is no more than n p and the average latency of users accessing p is no more than 6C p while ensuring that the capacity constraints are violated by at most a factor of 4. We use the LP rounding scheme described in [5, 2]. No copy of an object has more than 4d p users assigned to it. Consider any open instance o p of object p. Let U op denote the users mapped to this object, and S op denote the set of fractional objects closed while opening o p . The rounding scheme maintains the following properties: 1. There ....

J.-H. Lin and J. S. Vitter. -approximations with minimum packing constraint violations. Proceedings of 24th ACM STOC, 1992.

....increasing the cost by at most a factor of 12. Furthermore, in the case where all the f i = 0, we can get an improved approximation guarantee of 10. Proof: The basic idea of the rounding algorithm is similar to the one given by Shmoys et al. 21] The algorithm first performs a filtering step [15, 16] followed by clustering, after which a facility is chosen from each cluster. By the properties of the filtering, the cost of opening this facility and connecting the demand points to it is not much more than the fractional cost. However, showing that a near optimal Steiner tree connecting these ....

Jyh-Han Lin and Jeffrey Scott Vitter. #-approximations with minimum packing constraint violation (extended abstract). In Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 771--782, 1992.

....of a # approximation algorithm with # 1.46 would imply that P = NP. The first constant factor approximation algorithm for the metric uncapacitated facility location problem was developed by Shmoys, Tardos Aardal [ STA97] and was based on the filtering technique introduced by Lin Vitter[ LV92] The performance guarantee of this algorithm is 3.16. Their result was subsequently improved by Guha Khuller[ GK98] who obtained a 2.41 approximation algorithm applying a greedy procedure to the solution obtained by [ STA97] and by Chudak Shmoys [ C98] who provided an 1.73 approximation ....

J. H. Lin and J. S. Vitter. #-approximation with minimum packing constraint violation. Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 771-782, 1992

....increasing the cost by at most a factor of 12. Furthermore, in the case where all the f i = 0, we can get an improved approximation guarantee of 9.002. Proof: The basic idea of the rounding algorithm is similar to the one given by Shmoys et al. 22] The algorithm first performs a filtering step [16, 17] followed by clustering, after which a facility is chosen from each cluster. By the properties of the filtering, the cost of opening this facility and connecting the demand points to it is not much more than the fractional cost. However, showing that a near optimal Steiner tree connecting these ....

Jyh-Han Lin and Jeffrey Scott Vitter. #-approximations with minimum packing constraint violation (extended abstract). In Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 771--782, 1992.

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J.-H. Lin and J. S. Vitter. #-approximations with minimum packing constraint violation. In Proceedings of the ACM Symposium on Theory of Computing, pages 771--782, 1992.

No context found.

J. H. Lin and J. S. Vitter. -approximations with minimum packing constraint violation. In Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 771-782, 1992.

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J. H. Lin and J. S. Vitter. #-approximations with minimum packing constraint violation. In Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 771--782, 1992.

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J.-H. Lin and J. S. Vitter. -approximations with minimum packing constraint violations. Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing, 1992.

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J.-H. Lin and J. S. Vitter. "-approximations with minimum packing constraint violation. In Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 771--782, May 1992.

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J.-H. Lin and J. S. Vitter. -approximations with minimum packing constraint violation. In STOC'92, Victoria, B.C., Canada, 1992.

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Jyh-Han Lin and Je#rey Scott Vitter, "#-approximations with minimum packing constraint violation," in STOC'92, Victoria, B.C., Canada, 1992.

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J. H. Lin and J. S. Vitter. -approximations with minimum packing constraint violations. Proc. STOC, 1992.

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J-H. Lin and J.S. Vitter. "#-approximations with minimum packing constraint violation," Proceedings of the 24th Annual ACM Symposium on the Theory of Computing, 1992, pp. 771-782.

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J.-H. Lin and J. S. Vitter. "-Approximations with minimum packing constraint violation. In Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 771--782, May 1992.

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