منابع مشابه
Approximating set multi-covers
Lovász and Stein (independently) proved that any hypergraph satisfies τ ≤ (1+ln ∆)τ * , where τ is the transversal number, τ * is its fractional version, and ∆ denotes the maximum degree. We prove τ f ≤ 3.17τ * max{ln ∆, f } for the f-fold transversal number τ f. Similarly to Lovász and Stein, we also show that this bound can be achieved non-probabilistically, using a greedy algorithm. As a com...
متن کاملApproximating Minimum Power Edge-Multi-Covers
Given a graph with edge costs, the power of a node is the maximum cost of an edge incident to it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless networks, we consider the following fundamental problem in wireless network design. Given a graph G = (V,E) with edge costs and degree bounds {r(v) : v ∈ V }, the Minimum-Power Edge-Multi-Cover (MP...
متن کاملOn Approximating Restricted Cycle Covers
A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle. An L-cycle cover is a cycle cover in which the length of every cycle is in the set L. A special case of L-cycle covers are k-cycle covers for k ∈ N, where the length of each cycle must be at least k. The weight of a cycle cover of an edge-weighted graph is the sum of the weights of its edges. We com...
متن کاملOn Approximating Target Set Selection
We study the Target Set Selection (TSS) problem introduced by Kempe, Kleinberg, and Tardos (2003). This problem models the propagation of influence in a network, in a sequence of rounds. A set of nodes is made “active” initially. In each subsequent round, a vertex is activated if at least a certain number of its neighbors are (already) active. In the minimization version, the goal is to activat...
متن کاملApproximating the Tree and Tour Covers of a Graph
The tree and tour cover problems on an edge-weighted graph are to compute a minimum weight tree and closed walk, respectively, whose vertices form a vertex cover. Both problems are NP-hard. In this note we give strongly polynomial time, constant factor approximation algorithms for both problems. An interesting feature of our algorithms is how they combine approximations of other problems, namel...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2018
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2017.08.001