646 research outputs found
A Note on: `Algorithms for Connected Set Cover Problem and Fault-Tolerant Connected Set Cover Problem'
A flaw in the greedy approximation algorithm proposed by Zhang et al. for
minimum connected set cover problem is corrected, and a stronger result on the
approximation ratio of the modified greedy algorithm is established. The
results are now consistent with the existing results on connected dominating
set problem which is a special case of the minimum connected set cover problem.Comment: 6 pages, 1 figure, submitted to Theoretical Computer Scienc
Improved Approximation Algorithm for Minimum-Weight --Connected Dominating Set
The classical minimum connected dominating set (MinCDS) problem aims to find
a minimum-size subset of connected nodes in a network such that every other
node has at least one neighbor in the subset. This problem is drawing
considerable attention in the field of wireless sensor networks because
connected dominating sets can serve as virtual backbones of such networks.
Considering fault-tolerance, researchers developed the minimum -connected
-fold CDS (MinCDS) problem. Many studies have been conducted on
MinCDSs, especially those in unit disk graphs. However, for the minimum-weight
CDS (MinWCDS) problem in general graphs, algorithms with guaranteed
approximation ratios are rare. Guha and Khuller designed a
-approximation algorithm for MinWCDS, where is the
number of nodes. In this paper, we improved the approximation ratio to
for MinWCDS, where is the
maximum degree of the graph
Remote spanners: what to know beyond neighbors
International audienceMotivated by the fact that neighbors are generally known in practical routing algorithms, we introduce the notion of remote-spanner. Given an unweighted graph , a sub-graph with vertex set is an \emph{(\a,\b)-remote-spanner} if for each pair of points and the distance between and in , the graph augmented by all the edges between and its neighbors in , is at most \a times the distance between and in plus \b. We extend this definition to -connected graphs by considering minimum length sum over disjoint paths as distance. We then say that an (\a,\b)-remote-spanner is \emph{-connecting }. In this paper, we give distributed algorithms for computing (1+\eps,1-2\eps)-remote-spanners for any \eps>0, -connecting -remote-spanners for any (yielding -remote-spanners for ) and -connecting -remote-spanners. All these algorithms run in constant time for any unweighted input graph. The number of edges obtained for -connecting -remote-spanner is within a logarithmic factor from optimal (compared to the best -connecting -remote-spanner of the input graph). Interestingly, sparse -remote-spanners (i.e. preserving exact distances) with edges exist in random unit disk graphs. The number of edges obtained for (1+\eps,1-2\eps)-remote-spanners and -connecting -remote-spanners is linear if the input graph is the unit ball graph of a doubling metric (distances between nodes are unknown). Our methodology consists in characterizing remote-spanners as sub-graphs containing the union of small depth tree sub-graphs dominating nearby nodes. This leads to simple local distributed algorithms
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