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- W2741373816 abstract "Consider a graph with n nodes V = {1, 2 ,...,n } and let d(i, j) denote the distance between nodes i, j. Given a permutation π on {1, 2 ,...,n } such that π(1) = 1, the back-walk-free latency from node 1t o nodej is defined by � π(j )= � π(j − 1) + min{d(π(k) ,π (j)) | 1 ≤ k ≤ j − 1}. Note that � π(1) = d(1, 1) = 0. Each vertex i is associated with a nonnegative weight w(i). The (weighted) minimum back-walk-free latency problem (MBLP) is to find a permutation π such that the total back-walk-free latency n=1 w(i)� π(i) is minimized. In this paper, we show an O(n log n) time algorithm when the given graph is a tree. For a k-path trees, we derive an O(n log k) time algorithm; the algorithm is shown to be optimal in term of time complexity on any comparison based computational model. Further, we show that the optimal tour on weighted paths can be found in O(n) time. No previous hardness results were known for MBLP on general graphs. Here we settle the problem by showing that MBLP is NP-complete even when the given graph is a direct acyclic graph whose vertex weights are either 0 or 1." @default.
- W2741373816 created "2017-08-08" @default.
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- W2741373816 date "2002-01-01" @default.
- W2741373816 modified "2023-09-23" @default.
- W2741373816 title "Minimum Back-Walk-Free Latency Problem (Extended Abstract)" @default.
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