Secluded Path via Shortest Path
Lecture Notes in Computer Science(2014)
摘要
We provide several new algorithmic results for the secluded path problem, specifically approximation and optimality results for the static algorithm of [3,5], and an extension (h-Memory) of it based on de Bruijn graphs, when applied to bounded degree graphs and some other special graph classes which can model wireless communication and line-of-sight settings. Our primary result is that h-Memory is a PTAS for degree-Δ unweighted, undirected graphs, providing a \(\lceil{\sqrt{{\Delta+1}\over{h+1}}}\rceil\)-approximation in time O(n logn); in particular, 0-Memory (i.e., static) provides a \(\sqrt{\Delta+1}\) -approximation (i.e., \(\epsilon=\sqrt{\Delta+1}-1\)), tightening the previous analysis of this algorithm, and Δ-Memory is optimal (i.e., ε = 0), and is faster than the known optimal algorithm for this setting [3].
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