TY - GEN

T1 - Approximation algorithms and hardness results for labeled connectivity problems

AU - Hassin, Refael

AU - Monnot, Jérôme

AU - Segev, Danny

PY - 2006

Y1 - 2006

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 ℕ to which at least one edge is mapped has 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 1 ⊆ ℕ such that the edge set (e ∈ E : (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, where s and t are provided as part of the input. The main contributions of this paper are improved approximation algorithms and hardness results for MinLST and MinLP. As a secondary objective, we make a concentrated effort to relate the algorithmic methods utilized in approximating these problems to a number of well-known techniques, originally studied in the context of integer covering.

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 ℕ to which at least one edge is mapped has 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 1 ⊆ ℕ such that the edge set (e ∈ E : (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, where s and t are provided as part of the input. The main contributions of this paper are improved approximation algorithms and hardness results for MinLST and MinLP. As a secondary objective, we make a concentrated effort to relate the algorithmic methods utilized in approximating these problems to a number of well-known techniques, originally studied in the context of integer covering.

UR - http://www.scopus.com/inward/record.url?scp=33750060997&partnerID=8YFLogxK

U2 - 10.1007/11821069_42

DO - 10.1007/11821069_42

M3 - Conference contribution

AN - SCOPUS:33750060997

SN - 3540377913

SN - 9783540377917

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 480

EP - 491

BT - Mathematical Foundations of Computer Science 2006 - 31st International Symposium, MFCS 2006, Proceedings

PB - Springer Verlag

T2 - 31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006

Y2 - 28 August 2006 through 1 September 2006

ER -