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- W2020164139 abstract "We consider some network design problems with applications for wireless networks. The input for these problems is a metric space (X,d) and a finite subset U⊆X of terminals. In the Steiner Tree with Minimum Number of Steiner Points (STMSP) problem, the goal is to find a minimum size set S⊆X−U of points so that the unit-disc graph of S+U is connected. Let Δ be the smallest integer so that for any finite V⊆X for which the unit-disc graph is connected, this graph contains a spanning tree with maximum degree ⩽Δ. The best known approximation ratio for STMSP was Δ−1 [I.I. Măndoiu, A.Z. Zelikovsky, A note on the MST heuristic for bounded edge-length Steiner trees with minimum number of Steiner points, Information Processing Letters 75 (4) (2000) 165–167]. We improve this ratio to ⌊(Δ+1)/2⌋+1+ε. In the Minimum Power Spanning Tree (MPST) problem, V=X is finite, and the goal is to find a “range assignment” {p(v):v∈V} on the nodes so that the edge set {uv∈E:d(uv)⩽min{p(u),p(v)}} contains a spanning tree, and ∑v∈Vp(v) is minimized. We consider a particular case {0,1}-MPST of MPST when the distances are in {0,1}; here the goal is to find a minimum size set S⊆V of “active” nodes so that the graph (V,E0+E1(S)) is connected, where E0={uv:d(uv)=0}, and E1(S) is the set the edges in E1={uv:d(uv)=1} with both endpoints in S. We will show that the (5/3+ε)-approximation scheme for MPST of [E. Althaus, G. Calinescu, I. Măndoiu, S. Prasad, N. Tchervenski, A. Zelikovsky, Power efficient range assignment for symmetric connectivity in static ad hoc wireless networks, Wireless Networks 12 (3) (2006) 287–299] achieves a ratio 3/2 for {0,1}-distances. This answers an open question posed in [E. Lloyd, R. Liu, S. Ravi, Approximating the minimum number of maximum power users in ad hoc networks, Mobile Networks and Applications 11 (2006) 129–142]." @default.
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- W2020164139 date "2009-09-01" @default.
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- W2020164139 title "Wireless network design via 3-decompositions" @default.
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