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Exact Algorithms for Set Multicover and Multiset Multicover Problems
"... Abstract. Given a universe N containing n elements and a collection of multisets or sets over N, the multiset multicover (MSMC) or the set multicover (SMC) problem is to cover all elements at least a number of times as specified in their coverage requirements with the minimum number of multisets or ..."
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Cited by 2 (1 self)
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or sets. In this paper, we give various exact algorithms for these two problems, with or without constraints on the number of times a multiset or set may be picked. First, we can exactly solve the MSMC without multiplicity constraints problem in O(((b +1)(c +1)) n) time where b and c (c ≤ b and b ≥ 2
On the Set MultiCover Problem in Geometric Settings
 IN PROC. 25TH ANNU. ACM SYMPOS. COMPUT. GEOM
, 2009
"... We consider the set multicover problem in geometric settings. Given a set of points P and a collection of geometric shapes (or sets) F, we wish to nd a minimum cardinality subset of F such that each point p ∈ P is covered by (contained in) at least d(p) sets. Here d(p) is an integer demand (require ..."
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Cited by 19 (4 self)
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We consider the set multicover problem in geometric settings. Given a set of points P and a collection of geometric shapes (or sets) F, we wish to nd a minimum cardinality subset of F such that each point p ∈ P is covered by (contained in) at least d(p) sets. Here d(p) is an integer demand
Set MultiCovering via InclusionExclusion
"... Set multicovering is a generalization of the set covering problem where each element may need to be covered more than once and thus some subset in the given family of subsets may be picked several times for minimizing the number of sets to satisfy the coverage requirement. In this paper, we propose ..."
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Cited by 3 (2 self)
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propose a family of exact algorithms for the set multicovering problem based on the inclusionexclusion principle. The presented ESMC (Exact Set MultiCovering) algorithm takes * n O ((2 t) ) time and * n O ( ( t + 1) ) space where t is the maximum value in the coverage requirement set (The * O ( f ( n
Partial Multicovering and the dconsecutive Ones Property
, 2011
"... A dinterval is the union of d disjoint intervals on the real line. In the dinterval stabbing problem (dis) we are given a set of dintervals and a set of points, each dinterval I has a stabbing requirement r(I) and each point has a weight, and the goal is to find a minimum weight multiset of poi ..."
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A dinterval is the union of d disjoint intervals on the real line. In the dinterval stabbing problem (dis) we are given a set of dintervals and a set of points, each dinterval I has a stabbing requirement r(I) and each point has a weight, and the goal is to find a minimum weight multiset
Primaldual rnc approximation algorithms for (multi)set (multi)cover and covering integer programs
 SIAM J. on Computing
, 1993
"... Abstract. We build on the classical greedy sequential set cover algorithm, in the spirit of the primaldual schema, to obtain simple parallel approximation algorithms for the set cover problem and its generalizations. Our algorithms use randomization, and our randomized voting lemmas may be of indep ..."
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Cited by 23 (0 self)
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Abstract. We build on the classical greedy sequential set cover algorithm, in the spirit of the primaldual schema, to obtain simple parallel approximation algorithms for the set cover problem and its generalizations. Our algorithms use randomization, and our randomized voting lemmas may
A Multicover Nerve for Geometric Inference
"... We show that filtering the barycentric decomposition of a Čech complex by the cardinality of the vertices captures precisely the topology of kcovered regions among a collection of balls for all values of k. Moreover, we relate this result to the VietorisRips complex to get an approximation in term ..."
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Cited by 4 (1 self)
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We show that filtering the barycentric decomposition of a Čech complex by the cardinality of the vertices captures precisely the topology of kcovered regions among a collection of balls for all values of k. Moreover, we relate this result to the VietorisRips complex to get an approximation in terms of the persistent homology. 1
Bucket game with applications to set multicover and dynamic page migration
 in: Proc. of the 13th European Symp. on Algorithms (ESA
, 2005
"... Abstract. We present a simple twoperson Bucket Game, based on throwing balls into buckets, and we discuss possible players ’ strategies. We use these strategies to create an approximation algorithm for a generalization of the well known Set Cover problem, where we need to cover each element by at ..."
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Cited by 5 (4 self)
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Abstract. We present a simple twoperson Bucket Game, based on throwing balls into buckets, and we discuss possible players ’ strategies. We use these strategies to create an approximation algorithm for a generalization of the well known Set Cover problem, where we need to cover each element
unknown title
"... ABSTRACT: Minwise independence is a recently introduced notion of limited independence,similar in spirit to pairwise independence. The latter has proven essential for the derandomization of many algorithms. Here we show that approximate minwise independence allows similaruses, by presenting a dera ..."
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derandomization of the RNC algorithm for approximate set cover due to S. Rajagopalan and V. Vazirani. We also discuss how to derandomize their set multicover andmultiset multicover algorithms in restricted cases. The multicover case leads us to discuss the concept of kminimawise independence, a natural
A Derandomization Using MinWise Independent Permutations
 In Randomization and approximation techniques in computer science
"... . Minwise independence is a recently introduced notion of limited independence, similar in spirit to pairwise independence. The later has proven essential for the derandomization of many algorithms. Here we show that approximate minwise independence allows similar uses, by presenting a derando ..."
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Cited by 20 (3 self)
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derandomization of the RNC algorithm for approximate set cover due to S. Rajagopalan and V. Vazirani. We also discuss how to derandomize their set multicover and multiset multicover algorithms in restricted cases. The multicover case leads us to discuss the concept of kminimawise independence, a natural
Approximation Algorithms For Set Cover And Related Problems
, 1998
"... In this thesis, we analyze several known and newly designed algorithms for approximating optimal solutions to NPhard optimization problems. We give a new analysis of the greedy algorithm for approximating the Set Cover and Partial Set cover problems obtaining significantly improved performance boun ..."
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Cited by 12 (0 self)
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In this thesis, we analyze several known and newly designed algorithms for approximating optimal solutions to NPhard optimization problems. We give a new analysis of the greedy algorithm for approximating the Set Cover and Partial Set cover problems obtaining significantly improved performance
Results 1  10
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