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- W4302378613 abstract "In this paper, we study the $k$-forest problem in the model of resource augmentation. In the $k$-forest problem, given an edge-weighted graph $G(V,E)$, a parameter $k$, and a set of $m$ demand pairs $subseteq V times V$, the objective is to construct a minimum-cost subgraph that connects at least $k$ demands. The problem is hard to approximate---the best-known approximation ratio is $O(min{sqrt{n}, sqrt{k}})$. Furthermore, $k$-forest is as hard to approximate as the notoriously-hard densest $k$-subgraph problem. While the $k$-forest problem is hard to approximate in the worst-case, we show that with the use of resource augmentation, we can efficiently approximate it up to a constant factor. First, we restate the problem in terms of the number of demands that are {em not} connected. In particular, the objective of the $k$-forest problem can be viewed as to remove at most $m-k$ demands and find a minimum-cost subgraph that connects the remaining demands. We use this perspective of the problem to explain the performance of our algorithm (in terms of the augmentation) in a more intuitive way. Specifically, we present a polynomial-time algorithm for the $k$-forest problem that, for every $epsilon>0$, removes at most $m-k$ demands and has cost no more than $O(1/epsilon^{2})$ times the cost of an optimal algorithm that removes at most $(1-epsilon)(m-k)$ demands." @default.
- W4302378613 created "2022-10-06" @default.
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- W4302378613 date "2016-11-22" @default.
- W4302378613 modified "2023-10-18" @default.
- W4302378613 title "Approximating k-Forest with Resource Augmentation: A Primal-Dual Approach" @default.
- W4302378613 doi "https://doi.org/10.48550/arxiv.1611.07489" @default.
- W4302378613 hasPublicationYear "2016" @default.
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