
Optimal Distributed Weighted Set Cover Approximation
We present a timeoptimal deterministic distributed algorithm for approx...
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A Deterministic Distributed 2Approximation for Weighted Vertex Cover in O( n/ ^2) Rounds
We present a deterministic distributed 2approximation algorithm for the...
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A Faster FPTAS for #Knapsack
Given a set W = {w_1,..., w_n} of nonnegative integer weights and an in...
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An O(1)Approximation Algorithm for Dynamic Weighted Vertex Cover with Soft Capacity
This study considers the (soft) capacitated vertex cover problem in a dy...
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Largest Weight Common Subtree Embeddings with Distance Penalties
The largest common embeddable subtree problem asks for the largest possi...
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Finding Closed Quasigeodesics on Convex Polyhedra
A closed quasigeodesic is a closed loop on the surface of a polyhedron w...
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NearOptimal Algorithms for PointLine Covering Problems
We study fundamental pointline covering problems in computational geome...
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Optimal Distributed Covering Algorithms
We present a timeoptimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank f. This problem is equivalent to the Minimum Weight Set Cover problem in which the frequency of every element is bounded by f. The approximation factor of our algorithm is (f+ϵ). Our algorithm runs in the CONGEST model and requires O(Δ/ Δ) rounds, for constants ϵ∈(0,1] and f∈ N^+. This is the first distributed algorithm for this problem whose running time does not depend on the vertex weights nor the number of vertices. For constant values of f and ϵ, our algorithm improves over the (f+ϵ)approximation algorithm of KMW06 whose running time is O(Δ + W), where W is the ratio between the largest and smallest vertex weights in the graph. Our algorithm also achieves an fapproximation for the problem in O(f n) rounds, improving over the classical result of KVY94 that achieves a running time of O(f^2 n). Finally, for weighted vertex cover (f=2) our algorithm achieves a deterministic running time of O( n), matching the randomized previously best result of KY11. We also show that integer coveringprograms can be reduced to the Minimum Weight Set Cover problem in the distributed setting. This allows us to achieve an (f+ϵ)approximate integral solution in O(Δ/Δ+(f· M)^1.01ϵ^1(Δ)^0.01) rounds, where f bounds the number of variables in a constraint, Δ bounds the number of constraints a variable appears in, and M={1, 1/a_}, where a_min is the smallest normalized constraint coefficient. This improves over the results of KMW06 for the integral case, which runs in O(ϵ^4· f^4· f·(M·Δ)) rounds.
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