Approximating max-min linear programs with local algorithms
| Autor: | Floréen, Patrik, Kaski, Petteri, Musto, Topi, Suomela, Jukka |
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| Rok vydání: | 2007 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1109/IPDPS.2008.4536235 |
| Popis: | A local algorithm is a distributed algorithm where each node must operate solely based on the information that was available at system startup within a constant-size neighbourhood of the node. We study the applicability of local algorithms to max-min LPs where the objective is to maximise $\min_k \sum_v c_{kv} x_v$ subject to $\sum_v a_{iv} x_v \le 1$ for each $i$ and $x_v \ge 0$ for each $v$. Here $c_{kv} \ge 0$, $a_{iv} \ge 0$, and the support sets $V_i = \{v : a_{iv} > 0 \}$, $V_k = \{v : c_{kv}>0 \}$, $I_v = \{i : a_{iv} > 0 \}$ and $K_v = \{k : c_{kv} > 0 \}$ have bounded size. In the distributed setting, each agent $v$ is responsible for choosing the value of $x_v$, and the communication network is a hypergraph $\mathcal{H}$ where the sets $V_k$ and $V_i$ constitute the hyperedges. We present inapproximability results for a wide range of structural assumptions; for example, even if $|V_i|$ and $|V_k|$ are bounded by some constants larger than 2, there is no local approximation scheme. To contrast the negative results, we present a local approximation algorithm which achieves good approximation ratios if we can bound the relative growth of the vertex neighbourhoods in $\mathcal{H}$. Comment: 16 pages, 2 figures |
| Databáze: | arXiv |
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