TY - JOUR

T1 - Approximation algorithms and hardness results for labeled connectivity problems

AU - Hassin, Refael

AU - Monnot, Jérôme

AU - Segev, Danny

PY - 2007/11

Y1 - 2007/11

N2 - Let G=(V,E) be a connected multigraph, whose edges are associated with labels specified by an integer-valued function E → ℕ. In addition, each label l ε ℕ a non-negative cost c(l). The minimum label spanning tree problem (MinLST) asks to find a spanning tree in G that minimizes the overall cost of the labels used by its edges. Equivalently, we aim at finding a minimum cost subset of labels I ⊆ ℕ such that the edge set {e ∈ E: L (e) ∈ I} forms a connected subgraph spanning all vertices. Similarly, in the minimum label s - t path problem (MinLP) the goal is to identify an s-t path minimizing the combined cost of its labels. The main contributions of this paper are improved approximation algorithms and hardness results for MinLST and MinLP.

AB - Let G=(V,E) be a connected multigraph, whose edges are associated with labels specified by an integer-valued function E → ℕ. In addition, each label l ε ℕ a non-negative cost c(l). The minimum label spanning tree problem (MinLST) asks to find a spanning tree in G that minimizes the overall cost of the labels used by its edges. Equivalently, we aim at finding a minimum cost subset of labels I ⊆ ℕ such that the edge set {e ∈ E: L (e) ∈ I} forms a connected subgraph spanning all vertices. Similarly, in the minimum label s - t path problem (MinLP) the goal is to identify an s-t path minimizing the combined cost of its labels. The main contributions of this paper are improved approximation algorithms and hardness results for MinLST and MinLP.

KW - Approximation algorithms

KW - Hardness of approximation

KW - Labeled connectivity

UR - http://www.scopus.com/inward/record.url?scp=34848849832&partnerID=8YFLogxK

U2 - 10.1007/s10878-007-9044-x

DO - 10.1007/s10878-007-9044-x

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AN - SCOPUS:34848849832

VL - 14

SP - 437

EP - 453

JO - Journal of Combinatorial Optimization

JF - Journal of Combinatorial Optimization

SN - 1382-6905

IS - 4

ER -