Approximation of Pareto optima in multiple-objective, shortest-path problems
Operations Research
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Approximation schemes for the restricted shortest path problem
Mathematics of Operations Research
The network inhibition problem
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Design networks with bounded pairwise distance
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Steiner tree problem with minimum number of Steiner points and bounded edge-length
Information Processing Letters
Approximation algorithms for directed Steiner problems
Journal of Algorithms
Information Processing Letters
K-pair delay constrained minimum cost routing in undirected networks
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximations for Steiner Trees with Minimum Number of Steiner Points
Journal of Global Optimization
An improved FPTAS for restricted shortest path
Information Processing Letters
Relay sensor placement in wireless sensor networks
Wireless Networks
The subdivision-constrained minimum spanning tree problem
Theoretical Computer Science
Set connectivity problems in undirected graphs and the directed steiner network problem
ACM Transactions on Algorithms (TALG)
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We are given a digraph D=(V,A;w), a length (delay) function w:A驴R +, a positive integer d and a set $\mathcal{P}=\{(s_{i},t_{i};B_{i}) | i=1,2,\ldots,k\}$ of k requests, where s i 驴V is called as the ith source node, t i 驴V is called the ith sink node and B i is called as the ith length constraint. For a given positive integer d, the subdivision-constrained routing requests problem (SCRR, for short) is to find a directed subgraph D驴=(V驴,A驴) of D, satisfying the two constraints: (1) Each request (s i ,t i ;B i ) has a path P i from s i to t i in D驴 with length $w(P_{i})=\sum_{e\in P_{i}} w(e)$ no more than B i ; (2) Insert some nodes uniformly on each arc e驴A驴 to ensure that each new arc has length no more than d. The objective is to minimize the total number of the nodes inserted on the arcs in A驴.We obtain the following three main results: (1) The SCRR problem is at least as hard as the set cover problem even if each request has the same source s, i.e., s i =s for each i=1,2,驴,k; (2) For each request (s,t;B), we design a dynamic programming algorithm to find a path from s to t with length no more than B such that the number of the nodes inserted on such a path is minimized, and as a corollary, we present a k-approximation algorithm to solve the SCRR problem for any k requests; (3) We finally present an optimal algorithm for the case where $\mathcal{P}$ contains all possible requests (s i ,t i ) in V脳V and B i is equal to the length of the shortest path in D from s i to t i . To the best of our knowledge, this is the first time that the dynamic programming algorithm within polynomial time in (2) is designed for a weighted optimization problem while previous optimal algorithms run in pseudo-polynomial time.