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- W2951117415 abstract "In Source Location (SL) problems the goal is to select a mini-mum cost source set $S subseteq V$ such that the connectivity (or flow) $psi(S,v)$ from $S$ to any node $v$ is at least the demand $d_v$ of $v$. In many SL problems $psi(S,v)=d_v$ if $v in S$, namely, the demand of nodes selected to $S$ is completely satisfied. In a node-connectivity variant suggested recently by Fukunaga, every node $v$ gets a $p_v leq d_v$ if it is selected to $S$. Fukunaga showed that for undirected graphs one can achieve ratio $O(k ln k)$ for his variant, where $k=max_{v in V}d_v$ is the maximum demand. We improve this by achieving ratio $min{p^*lnk,k}cdot O(ln (k/q^*))$ for a more general version with node capacities, where $p^*=max_{v in V} p_v$ is the maximum bonus and $q^*=min_{v in V} q_v$ is the minimum capacity. In particular, for the most natural case $p^*=1$ considered by Fukunaga, we improve the ratio from $O(k ln k)$ to $O(ln^2k)$. We also get ratio $O(k)$ for the edge-connectivity version, for which no ratio that depends on $k$ only was known before. To derive these results, we consider a particular case of the Survivable Network (SN) problem when all edges of positive cost form a star. We give ratio $O(min{ln n,ln^2 k})$ for this variant, improving over the best ratio known for the general case $O(k^3 ln n)$ of Chuzhoy and Khanna." @default.
- W2951117415 created "2019-06-27" @default.
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- W2951117415 date "2012-10-17" @default.
- W2951117415 modified "2023-09-27" @default.
- W2951117415 title "Approximating Source Location and Star Survivable Network Problems" @default.
- W2951117415 hasPublicationYear "2012" @default.
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