Approximation schemes for the restricted shortest path problem
Mathematics of Operations Research
Efficient probabilistically checkable proofs and applications to approximations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A modified greedy heuristic for the set covering problem with improved worst case bound
Information Processing Letters
On approximation algorithms for the minimum satisfiability problem
Information Processing Letters
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
The minimum labeling spanning trees
Information Processing Letters
On the minimum label spanning tree problem
Information Processing Letters
The budgeted maximum coverage problem
Information Processing Letters
On the red-blue set cover problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A note on the minimum label spanning tree
Information Processing Letters
Distributions on Level-Sets with Applications to Approximation Algorithms
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
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Theory of Computing Systems
Local search for the minimum label spanning tree problem with bounded color classes
Operations Research Letters
A simple efficient approximation scheme for the restricted shortest path problem
Operations Research Letters
Worst-case behavior of the MVCA heuristic for the minimum labeling spanning tree problem
Operations Research Letters
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WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
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Let G = (V,E) be a connected multigraph, whose edges are associated with labels specified by an integer-valued function ${\mathcal{L}} : E \rightarrow \mathbb{N}$. 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 I⊆ℕ such that the edge set $\{ e \in E : {\mathcal {L}}( e ) \in I \}$ forms a connected subgraph spanning all vertices. Similarly, in the minimum label s-tpath 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.