14,238 research outputs found
Solving the k-center Problem Efficiently with a Dominating Set Algorithm
We present a polynomial time heuristic algorithm for the minimum dominating set problem. The algorithm can readily be used for solving the minimum alpha-all-neighbor dominating set problem and the minimum set cover problem. We apply the algorithm in heuristic solving the minimum k-center problem in polynomial time. Using a standard set of 40 test problems we experimentally show that our k-center algorithm performs much better than other well-known heuristics and is competitive with the best known (non-polynomial time) algorithms for solving the k-center problem in terms of average quality and deviation of the results as well as execution time
Approximation Algorithms for Polynomial-Expansion and Low-Density Graphs
We study the family of intersection graphs of low density objects in low
dimensional Euclidean space. This family is quite general, and includes planar
graphs. We prove that such graphs have small separators. Next, we present
efficient -approximation algorithms for these graphs, for
Independent Set, Set Cover, and Dominating Set problems, among others. We also
prove corresponding hardness of approximation for some of these optimization
problems, providing a characterization of their intractability in terms of
density
Distributed Symmetry Breaking in Hypergraphs
Fundamental local symmetry breaking problems such as Maximal Independent Set
(MIS) and coloring have been recognized as important by the community, and
studied extensively in (standard) graphs. In particular, fast (i.e.,
logarithmic run time) randomized algorithms are well-established for MIS and
-coloring in both the LOCAL and CONGEST distributed computing
models. On the other hand, comparatively much less is known on the complexity
of distributed symmetry breaking in {\em hypergraphs}. In particular, a key
question is whether a fast (randomized) algorithm for MIS exists for
hypergraphs.
In this paper, we study the distributed complexity of symmetry breaking in
hypergraphs by presenting distributed randomized algorithms for a variety of
fundamental problems under a natural distributed computing model for
hypergraphs. We first show that MIS in hypergraphs (of arbitrary dimension) can
be solved in rounds ( is the number of nodes of the
hypergraph) in the LOCAL model. We then present a key result of this paper ---
an -round hypergraph MIS algorithm in
the CONGEST model where is the maximum node degree of the hypergraph
and is any arbitrarily small constant.
To demonstrate the usefulness of hypergraph MIS, we present applications of
our hypergraph algorithm to solving problems in (standard) graphs. In
particular, the hypergraph MIS yields fast distributed algorithms for the {\em
balanced minimal dominating set} problem (left open in Harris et al. [ICALP
2013]) and the {\em minimal connected dominating set problem}. We also present
distributed algorithms for coloring, maximal matching, and maximal clique in
hypergraphs.Comment: Changes from the previous version: More references adde
A Branch-and-Reduce Algorithm for Finding a Minimum Independent Dominating Set
An independent dominating set D of a graph G = (V,E) is a subset of vertices
such that every vertex in V \ D has at least one neighbor in D and D is an
independent set, i.e. no two vertices of D are adjacent in G. Finding a minimum
independent dominating set in a graph is an NP-hard problem. Whereas it is hard
to cope with this problem using parameterized and approximation algorithms,
there is a simple exact O(1.4423^n)-time algorithm solving the problem by
enumerating all maximal independent sets. In this paper we improve the latter
result, providing the first non trivial algorithm computing a minimum
independent dominating set of a graph in time O(1.3569^n). Furthermore, we give
a lower bound of \Omega(1.3247^n) on the worst-case running time of this
algorithm, showing that the running time analysis is almost tight.Comment: Full version. A preliminary version appeared in the proceedings of WG
200
ND-Tree-based update: a Fast Algorithm for the Dynamic Non-Dominance Problem
In this paper we propose a new method called ND-Tree-based update (or shortly
ND-Tree) for the dynamic non-dominance problem, i.e. the problem of online
update of a Pareto archive composed of mutually non-dominated points. It uses a
new ND-Tree data structure in which each node represents a subset of points
contained in a hyperrectangle defined by its local approximate ideal and nadir
points. By building subsets containing points located close in the objective
space and using basic properties of the local ideal and nadir points we can
efficiently avoid searching many branches in the tree. ND-Tree may be used in
multiobjective evolutionary algorithms and other multiobjective metaheuristics
to update an archive of potentially non-dominated points. We prove that the
proposed algorithm has sub-linear time complexity under mild assumptions. We
experimentally compare ND-Tree to the simple list, Quad-tree, and M-Front
methods using artificial and realistic benchmarks with up to 10 objectives and
show that with this new method substantial reduction of the number of point
comparisons and computational time can be obtained. Furthermore, we apply the
method to the non-dominated sorting problem showing that it is highly
competitive to some recently proposed algorithms dedicated to this problem.Comment: 15 pages, 21 figures, 3 table
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