Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Approximating the minimum-degree Steiner tree to within one of optimal
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
A network-flow technique for finding low-weight bounded-degree spanning trees
Journal of Algorithms
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Computing Minimum-Weight Perfect Matchings
INFORMS Journal on Computing
Primal-dual meets local search: approximating MST's with nonuniform degree bounds
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Integrated topology control and routing in wireless optical mesh networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
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Traditional shortest path problems play a central role in both the design and use of communication networks and have been studied extensively. In this work, we consider a variant of the shortest path problem. The network has two kinds of edges, “actual” edges and “potential” edges. In addition, each vertex has a degree/interface constraint. We wish to compute a shortest path in the graph that maintains feasibility when we convert the potential edges on the shortest path to actual edges. The central difficulty is when a node has only one free interface, and the unconstrained shortest path chooses two potential edges incident on this node. We first show that this problem can be solved in polynomial time by reducing it to the minimum weighted perfect matching problem. The number of steps taken by this algorithm is O(|E|2 log |E|) for the single-source single-destination case. In other words, for each v we compute the shortest path Pv such that converting the potential edges on Pv to actual edges, does not violate any degree constraint. We then develop more efficient algorithms by extending Dijkstra’s shortest path algorithm. The number of steps taken by the latter algorithm is O(|E||V|), even for the single-source all destination case.