Greedy ${\ensuremath{\Delta}}$ -Approximation Algorithm for Covering with Arbitrary Constraints and Submodular Cost

Koufogiannakis, Christos; Young, Neal E.

doi:10.1007/978-3-642-02927-1_53

Cited by 15 publications

(7 citation statements)

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“…Approximating SM-vertex cover has been a subject of previous research work. Three different 2approximation algorithms were devised for the problem: Koufogiannakis and Young [KY09] devised approximations for SM-"covering" problems with monotone submodular objective function. The approximation algorithm is based on the frequency technique (called maximal dual feasible technique in [Hoc97] Ch.…”

Section: Related Researchmentioning

confidence: 99%

Complexity and approximations for submodular minimization problems on two variables per inequality constraints

Hochbaum

2018

Discrete Applied Mathematics

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Section: Related Researchmentioning

confidence: 99%

Complexity and approximations for submodular minimization problems on two variables per inequality constraints

Hochbaum

2018

Discrete Applied Mathematics

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“…Koufogiannakis and Young [14] present a deterministic greedy ∆-approximation algorithm for any covering problem with a submodular and non-decreasing objective function, and with arbitrary constraints that are closed upwards, such that each constraint has at most ∆ variables. They show that their algorithm is ∆-competitive for the online version of the problem where the constraints are revealed one at a time.…”

Section: Previous Workmentioning

confidence: 99%

“…These include LRU and FWF for paging, Balance and Greedy Dual for weighted caching, Landlord (a.k.a. Greedy Dual Size) for file caching, and algorithms for Connection Caching [14]. We study this approach and extend it to give deterministic online algorithms for the variants of online file caching studied in this paper.…”

Section: Previous Workmentioning

confidence: 99%

“…We present deterministic and randomized lower and upper bounds for these new variants of paging, weighted caching, and caching in the online setting. We use the approach in [14] to give deterministic algorithms for these online problems. While this approach is general, it doesn't necessarily give optimal online algorithms.…”

Section: Our Contributionsmentioning

confidence: 99%

“…In this section, we give a brief overview of the online covering approach from [14]. We use this approach, with modifications in some cases, to give deterministic algorithms for the variants of paging and caching problems in this paper.…”

Section: Online Covering Approachmentioning

confidence: 99%

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Caching with rental cost and zapping

Khare¹,

Young²

2012

Preprint

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The file caching problem is defined as follows. Given a cache of size k (a positive integer), the goal is to minimize the total retrieval cost for the given sequence of requests to files. A file f has size size(f ) (a positive integer) and retrieval cost cost(f ) (a non-negative number) for bringing the file into the cache. A miss or fault occurs when the requested file is not in the cache and the file has to be retrieved into the cache by paying the retrieval cost, and some other file may have to be removed (evicted ) from the cache so that the total size of the files in the cache does not exceed k.We study the following variants of the online file caching problem. Caching with Rental Cost (or Rental Caching ): There is a rental cost λ (a positive number) for each file in the cache at each time unit. The goal is to minimize the sum of the retrieval costs and the rental costs. Caching with Zapping : A file can be zapped by paying a zapping cost N ≥ 1. Once a file is zapped, all future requests of the file don't incur any cost. The goal is to minimize the sum of the retrieval costs and the zapping costs.We study these two variants and also the variant which combines these two (rental caching with zapping). We present deterministic lower and upper bounds in the competitive-analysis framework. We study and extend the online covering algorithm from [19] to give deterministic online algorithms. We also present randomized lower and upper bounds for some of these problems.

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Approximability of Sparse Integer Programs

Pritchard

Chakrabarty

2009

Lecture Notes in Computer Science

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The main focus of this paper is a pair of new approximation algorithms for certain integer programs. First, for covering integer programs {min cx: Ax >= b, 0 <= x <= d} where A has at most k nonzeroes per row, we give a k-approximation algorithm. (We assume A, b, c, d are nonnegative.) For any k >= 2 and eps>0, if P != NP this ratio cannot be improved to k-1-eps, and under the unique games conjecture this ratio cannot be improved to k-eps. One key idea is to replace individual constraints by others that have better rounding properties but the same nonnegative integral solutions; another critical ingredient is knapsack-cover inequalities. Second, for packing integer programs {max cx: Ax <= b, 0 <= x <= d} where A has at most k nonzeroes per column, we give a (2k^2+2)-approximation algorithm. Our approach builds on the iterated LP relaxation framework. In addition, we obtain improved approximations for the second problem when k=2, and for both problems when every A_{ij} is small compared to b_i. Finally, we demonstrate a 17/16-inapproximability for covering integer programs with at most two nonzeroes per column.Comment: Version submitted to Algorithmica special issue on ESA 2009. Previous conference version: http://dx.doi.org/10.1007/978-3-642-04128-0_

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Greedy ${\ensuremath{\Delta}}$ -Approximation Algorithm for Covering with Arbitrary Constraints and Submodular Cost

Cited by 15 publications

References 48 publications

Complexity and approximations for submodular minimization problems on two variables per inequality constraints

Complexity and approximations for submodular minimization problems on two variables per inequality constraints

Caching with rental cost and zapping

Approximability of Sparse Integer Programs

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