59,098 research outputs found

    Balancing Minimum Spanning and Shortest Path Trees

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    This paper give a simple linear-time algorithm that, given a weighted digraph, finds a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous trade-off: given the two trees and epsilon > 0, the algorithm returns a spanning tree in which the distance between any vertex and the root of the shortest-path tree is at most 1+epsilon times the shortest-path distance, and yet the total weight of the tree is at most 1+2/epsilon times the weight of a minimum spanning tree. This is the best tradeoff possible. The paper also describes a fast parallel implementation.Comment: conference version: ACM-SIAM Symposium on Discrete Algorithms (1993

    A Distributed Routing Algorithm for Internet-wide Geocast

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    Geocast is the concept of sending data packets to nodes in a specified geographical area instead of nodes with a specific address. To route geocast messages to their destination we need a geographic routing algorithm that can route packets efficiently to the devices inside the destination area. Our goal is to design an algorithm that can deliver shortest path tree like forwarding while relying purely on distributed data without central knowledge. In this paper, we present two algorithms for geographic routing. One based purely on distance vector data, and one more complicated algorithm based on path data. In our evaluation, we show that our purely distance vector based algorithm can come close to shortest path tree performance when a small number of routers are present in the destination area. We also show that our path based algorithm can come close to the performance of a shortest path tree in almost all geocast situations

    A Sidetrack-Based Algorithm for Finding the k Shortest Simple Paths in a Directed Graph

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    We present an algorithm for the k shortest simple path problem on weighted directed graphs (kSSP) that is based on Eppstein's algorithm for a similar problem in which paths are allowed to contain cycles. In contrast to most other algorithms for kSSP, ours is not based on Yen's algorithm and does not solve replacement path problems. Its worst-case running time is on par with state-of-the-art algorithms for kSSP. Using our algorithm, one may find O(m) simple paths with a single shortest path tree computation and O(n + m) additional time per path in well-behaved cases, where n is the number of nodes and m is the number of edges. Our computational results show that on random graphs and large road networks, these well-behaved cases are quite common and our algorithm is faster than existing algorithms by an order of magnitude. Further, the running time is far better predictable due to very small dispersion

    Log-space Algorithms for Paths and Matchings in k-trees

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    Reachability and shortest path problems are NL-complete for general graphs. They are known to be in L for graphs of tree-width 2 [JT07]. However, for graphs of tree-width larger than 2, no bound better than NL is known. In this paper, we improve these bounds for k-trees, where k is a constant. In particular, the main results of our paper are log-space algorithms for reachability in directed k-trees, and for computation of shortest and longest paths in directed acyclic k-trees. Besides the path problems mentioned above, we also consider the problem of deciding whether a k-tree has a perfect macthing (decision version), and if so, finding a perfect match- ing (search version), and prove that these two problems are L-complete. These problems are known to be in P and in RNC for general graphs, and in SPL for planar bipartite graphs [DKR08]. Our results settle the complexity of these problems for the class of k-trees. The results are also applicable for bounded tree-width graphs, when a tree-decomposition is given as input. The technique central to our algorithms is a careful implementation of divide-and-conquer approach in log-space, along with some ideas from [JT07] and [LMR07].Comment: Accepted in STACS 201

    A distributed shortest path algorithm for a planar network

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    AbstractAn algorithm is presented for finding a single source shortest path tree in a planar undirected distributed network with nonnegative edge costs. The number of messages used by the algorithm is O(n53) on an n-node network. Distributed algorithms are also presented for finding a breath-first spanning tree in general network, for finding a shortest path tree in a general network, for finding a separator of a planar network, and for finding a division of a planar network
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