Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Menger-type theorems with restrictions on path lengths
Discrete Mathematics
Short length versions of Menger's theorem
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Scheduling Algorithms
Length-bounded disjoint paths in planar graphs
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
Journal of Computer and System Sciences
On the complexity of vertex-disjoint length-restricted path problems
Computational Complexity
Graph Theory With Applications
Graph Theory With Applications
Improved bounds for the unsplittable flow problem
Journal of Algorithms
ACM Transactions on Algorithms (TALG)
Fast, Fair, and Efficient Flows in Networks
Operations Research
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Approximability of 3- and 4-hop bounded disjoint paths problems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Paths of bounded length and their cuts: Parameterized complexity and algorithms
Discrete Optimization
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For a given number L, an L-length-bounded edge-cut (node-cut, respectively) in a graph G with source s and sink t is a set C of edges (nodes, respectively) such that no s-t-path of length at most L remains in the graph after removing the edges (nodes, respectively) in C. An L-length-bounded flow is a flow that can be decomposed into flow paths of length at most L. In contrast to classical flow theory, we describe instances for which the minimum L-length-bounded edge-cut (node-cut, respectively) is Θ(n2/3)-times (Θ(&sqrt;n)-times, respectively) larger than the maximum L-length-bounded flow, where n denotes the number of nodes; this is the worst case. We show that the minimum length-bounded cut problem is NP-hard to approximate within a factor of 1.1377 for L≥ 5 in the case of node-cuts and for L≥ 4 in the case of edge-cuts. We also describe algorithms with approximation ratio O(min{L,n/L}) ⊆ O&sqrt;n in the node case and O(min {L,n2/L2,&sqrt;m} ⊆ O2/3 in the edge case, where m denotes the number of edges. Concerning L-length-bounded flows, we show that in graphs with unit-capacities and general edge lengths it is NP-complete to decide whether there is a fractional length-bounded flow of a given value. We analyze the structure of optimal solutions and present further complexity results.