Introduction to algorithms
The delivery man problem on a tree network
Annals of Operations Research
Power efficient filtering of data on air
EDBT '94 Proceedings of the 4th international conference on extending database technology: Advances in database technology
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Polynomial time algorithms for some minimum latency problems
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Data on Air: Organization and Access
IEEE Transactions on Knowledge and Data Engineering
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Optimal Index and Data Allocation in Multiple Broadcast Channels
ICDE '00 Proceedings of the 16th International Conference on Data Engineering
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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 驴 on {1, 2, . . . , n} such that 驴(1) = 1, the back-walk-free latency from node 1 to node j is defined by l驴(j) = l驴(j)- 1) + min{d(驴(k), 驴(j)) | 1 驴 k 驴 j - 1}. Note that l驴(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 驴 such that the total back-walk-free latency 驴ni=1 w(i)l驴(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.