Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Short length versions of Menger's theorem
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Improved bounds for the unsplittable flow problem
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Graph Theory With Applications
Graph Theory With Applications
Fast, Fair, and Efficient Flows in Networks
Operations Research
Maximizing total upload in latency-sensitive P2P applications
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Searching for a Visible, Lazy Fugitive
Graph-Theoretic Concepts in Computer Science
ACM Transactions on Algorithms (TALG)
Paths of bounded length and their cuts: Parameterized complexity and algorithms
Discrete Optimization
On effective TSV repair for 3D-stacked ICs
DATE '12 Proceedings of the Conference on Design, Automation and Test in Europe
Approximation algorithms for throughput maximization in wireless networks with delay constraints
IEEE/ACM Transactions on Networking (TON)
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An L-length-bounded cut in a graph G with source s, and sink t is a cut that destroys all s-t-paths of length at most L. An L-length-bounded flow is a flow in which only flow paths of length at most L are used. We show that the minimum length-bounded cut problem in graphs with unit edge lengths is $\mathcal{NP}$-hard to approximate within a factor of at least 1.1377 for L ≥5 in the case of node-cuts and for L ≥4 in the case of edge-cuts. We also give approximation algorithms of ratio min {L,n/L} in the node case and $\min\{L,n^2/L^2,\sqrt{m}\}$ in the edge case, where n denotes the number of nodes and m denotes the number of edges. We discuss the integrality gaps of the LP relaxations of length-bounded flow and cut problems, analyze the structure of optimal solutions, and present further complexity results for special cases.