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- W2113181958 abstract "We consider the problem of Single-Tiered Relay Placement with Basestations, which takes as input a set $$S$$ of sensors and a set $$B$$ of basestations described as points in a normed space $$(M,d)$$ , and real numbers $$0< rle R$$ . The objective is to place a minimum cardinality set $$Q$$ of wireless relay nodes that connects $$S$$ and $$B$$ according to the following rules. The sensors in $$S$$ can communicate within distance $$r$$ , relay nodes in $$Q$$ can communicate within distance $$R$$ , and basestations are considered to have an infinite broadcast range. Together the sets $$S, B$$ , and $$Q$$ induce an undirected graph $$G=(V,E)$$ defined as follows: $$V=Scup Bcup Q$$ and $$E={uv|u,vin B}cup {uv|uin Q$$ and $$vin Qcup B$$ and $$d(u,v)le R} cup {uv|uin S$$ and $$vin Scup Qcup B$$ and $$d(u,v)le r}$$ . Then $$Q$$ connects $$S$$ and $$B$$ when this induced graph is connected. In the case of the two-dimensional Euclidean plane, we get a $$(1+ln 6+epsilon )<2.8$$ -approximation algorithm, improving the previous best ratio of 3.11. Let $$varDelta $$ be the maximum number of points on a unit ball with pairwise distance strictly bigger than 1. Under certain assumptions, we have a $$left( 1+ln (varDelta +1)+epsilon right) $$ -approximation algorithm. When biconnectivity is required, we show that a variant of our previously proposed algorithm has approximation ratio of $$varDelta + 2$$ . In the case of the two-dimensional Euclidean plane, our ratio of 7 improves our previous bound of 16." @default.
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- W2113181958 date "2014-12-25" @default.
- W2113181958 modified "2023-10-18" @default.
- W2113181958 title "Improved approximation algorithms for single-tiered relay placement" @default.
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- W2113181958 doi "https://doi.org/10.1007/s10878-014-9823-0" @default.
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