Menger-type theorems with restrictions on path lengths
Discrete Mathematics
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
On the complexity of vertex-disjoint length-restricted path problems
Computational Complexity
Network design for vertex connectivity
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Inapproximability of survivable networks
Theoretical Computer Science
Paths of Bounded Length and Their Cuts: Parameterized Complexity and Algorithms
Parameterized and Exact Computation
Max Flow and Min Cut with bounded-length paths: complexity, algorithms, and approximation
Mathematical Programming: Series A and B - Series B - Special Issue: Combinatorial Optimization and Integer Programming
ACM Transactions on Algorithms (TALG)
On the k edge-disjoint 2-hop-constrained paths polytope
Operations Research Letters
Hop-level flow formulation for the hop constrained survivable network design problem
INOC'11 Proceedings of the 5th international conference on Network optimization
Benders Decomposition for the Hop-Constrained Survivable Network Design Problem
INFORMS Journal on Computing
| Hi-index | 0.00 |
A path is said to be ℓ-bounded if it contains at most ℓ edges. We consider two types of ℓ-bounded disjoint paths problems. In the maximum edge- or node-disjoint path problems MEDP(ℓ) and MNDP(ℓ), the task is to find the maximum number of edge- or node-disjoint ℓ-bounded (s,t)-paths in a given graph G with source s and sink t, respectively. In the weighted edge- or node-disjoint path problems WEDP(ℓ) and WNDP(ℓ), we are also given an integer k∈ℕ and non-negative edge weights ce∈ℕ, e∈E, and seek for a minimum weight subgraph of G that contains k edge- or node-disjoint ℓ-bounded (s,t)-paths. Both problems are of great practical relevance in the planning of fault-tolerant communication networks, for example. Even though length-bounded cut and flow problems have been studied intensively in the last decades, the $\mathcal{NP}$-hardness of some 3- and 4-bounded disjoint paths problems was still open. In this paper, we settle the complexity status of all open cases showing that WNDP(3) can be solved in polynomial time, that MEDP(4) is $\mathcal{AP\kern-1.5ptX}$-complete and approximable within a factor of 2, and that WNDP(4) and WEDP(4) are $\mathcal{AP\kern-1.5ptX}$-hard and $\mathcal{NPO}$-complete, respectively.