scholarly journals The Capacity Expansion Path Problem in Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Jianping Li ◽  
Juanping Zhu
Keyword(s):  
Shortest Path ◽  
Polynomial Algorithm ◽  
Shortest Paths ◽  
Minimum Cost ◽  
Capacity Expansion ◽  
Shortest Path Problem ◽  
Strongly Polynomial Algorithm ◽  
Minimum Number ◽  
Expansion Path ◽  
Strongly Polynomial

This paper considers the general capacity expansion path problem (GCEP) for the telecommunication operators. We investigate the polynomial equivalence between the GCEP problem and the constrained shortest path problem (CSP) and present a pseudopolynomial algorithm for the GCEP problem, no matter the graph is acyclic or not. Furthermore, we investigate two special versions of the GCEP problem. For the minimum number arc capacity expansion path problem (MN-CEP), we give a strongly polynomial algorithm based on the dynamic programming. For the minimum-cost capacity expansion shortest path problem (MCESP), we give a strongly polynomial algorithm by constructing a shortest paths network.

scholarly journals Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bingwu Zhang ◽  
Xiucui Guan ◽  
Chunyuan He ◽  
Shuguo Wang
Keyword(s):  
Polynomial Time ◽  
Shortest Path ◽  
Hamming Distance ◽  
Programming Model ◽  
Greedy Algorithms ◽  
Shortest Paths ◽  
Weighted Graph ◽  
Minimum Cost ◽  
Strongly Polynomial Time ◽  
Strongly Polynomial

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.

scholarly journals Efficient algorithms for the reverse shortest path problem on trees under the hamming distance

2017 ◽  
Vol 27 (1) ◽  
pp. 46-60 ◽  
Author(s):  
Javad Tayyebi ◽  
Massoud Aman
Keyword(s):  
Shortest Path ◽  
Hamming Distance ◽  
Minimum Cost ◽  
Shortest Path Problem ◽  
Arc Length ◽  
Bound Constraints ◽  
Shortest Distance ◽  
Special Cases ◽  
Minimum Cost Flow Problem ◽  
Minimum Cut Problem

Given a network G(V,A,c) and a collection of origin-destination pairs with prescribed values, the reverse shortest path problem is to modify the arc length vector c as little as possible under some bound constraints such that the shortest distance between each origin-destination pair is upper bounded by the corresponding prescribed value. It is known that the reverse shortest path problem is NP-hard even on trees when the arc length modifications are measured by the weighted sum-type Hamming distance. In this paper, we consider two special cases of this problem which are polynomially solvable. The first is the case with uniform lengths. It is shown that this case transforms to a minimum cost flow problem on an auxiliary network. An efficient algorithm is also proposed for solving this case under the unit sum-type Hamming distance. The second case considered is the problem without bound constraints. It is shown that this case is reduced to a minimum cut problem on a tree-like network. Therefore, both cases studied can be solved in strongly polynomial time.

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