The shortest path improvement problems under Hamming distance

This paper considers a selfish routing based network improvement problem, in which the authors would like to find a modified latency function that results in a new Nash equilibrium flow satisfying all traffic demands subject to the target capacity, while the total modification cost on edge latency is minimized. By using the reduction from the 3-Satisfiability (3-SAT) problem to our problem, the authors show that this problem is strongly NP-hard, even for the single commodity network.

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“…Let us construct a reduction from the 3-SAT problem to the decision version of the SRNI problem for a single commodity network [13] .…”

Section: Lemma 23 Will Imply That the Decision Version Of The Srni Pmentioning

confidence: 99%

A selfish routing based network improvement problem

Zhang

Fang

2011

J Syst Sci Complex

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“…Since the inverse optimization problems under Hamming distance were first studied by He et al [7], it has been investigated by many researchers (see, e.g., Zhang et al [8][9][10], Duin and Volgenant [11], Guan and Zhang [12], Liu and Yao [13], and Jiang et al [14]). Zhang et al [8] showed that the shortest path improvement problem under Hamming distance (denoted by SPIH) is strongly NP-hard on general graphs and is still NP-hard even if the network is a chain network. So it is meaningful to design polynomial time algorithms for some special cases of the problems and to propose approximation and/or heuristic algorithms for the SPIH and the shortest path improvement problem under unit Hamming distance (denoted by SPIUH) on general graphs.…”

Section: Introductionmentioning

confidence: 99%

Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance

Zhang

Guan

et al. 2013

Journal of Applied Mathematics

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In a shortest path improvement problem under unit Hamming distance (denoted by SPIUH), an edge weighted graph with a set of source-terminal pairs is given; we need to modify the lengths of edges by a minimum cost under unit Hamming distance such that the modified distances of the shortest paths are upper bounded by given values. The SPIUH problem on arborescent network is formulated as a 0-1 integer programming model. Some strongly polynomial time algorithms are designed for the problems on some special arborescent networks. Firstly, two greedy algorithms are proposed for problems on chain networks and special star-tree networks, respectively. Secondly, a strongly polynomial time algorithm is presented for the problem with a single source and constrained paths. Finally, a heuristic algorithm and its computational experiments are given for the SPIUH problem on general graphs.

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“…Since 1959, all theoretical developments in SSSP for general directed and undirected graphs have been based on Dijkstra's algorithm, visiting the vertices in order of increasing distance from s. As a matter of fact many real life problems can be represented as SSSP. As such, SSSP has been extensively applied in communication, computer systems, transportation networks and many other practical problems [1].…”

Section: Introductionmentioning

confidence: 99%

Two Phase Shortest Path Algorithm for Non-negative Weighted Undirected Graphs

Qureshi

Hassan

Safdar

et al. 2010

2010 Second International Conference on Communication Software and Networks

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In most of the shortest path problems like vehicle routing problems and network routing problems, we only need an efficient path between two points-source and destination, and it is not necessary to calculate the shortest path from source to all other nodes. This paper concentrates on this very idea and presents an algorithms for calculating shortest path for (i) nonnegative weighted undirected graphs (ii) unweighted undirected graphs. The algorithm completes its execution in O(|E|) for all graphs except few in which longer path (in terms of number of edges) from source to some node makes it best selection for that node.The main advantage of the algorithms is its simplicity and it does not need complex data structures for implementations.

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The shortest path improvement problems under Hamming distance

Cited by 24 publications

References 7 publications

A selfish routing based network improvement problem

A selfish routing based network improvement problem

Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance

Two Phase Shortest Path Algorithm for Non-negative Weighted Undirected Graphs

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