Introduction to algorithms
On the complexity of H-coloring
Journal of Combinatorial Theory Series B
Finding critical independent sets and critical vertex subsets are polynomial problems
SIAM Journal on Discrete Mathematics
On Finding Critical Independent and Vertex Sets
SIAM Journal on Discrete Mathematics
Improved Algorithms for Bipartite Network Flow
SIAM Journal on Computing
Bipartite graphs and their applications
Bipartite graphs and their applications
A combinatorial algorithm for weighted stable sets in bipartite graphs
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
The complexity of soft constraint satisfaction
Artificial Intelligence
Minimum cost and list homomorphisms to semicomplete digraphs
Discrete Applied Mathematics
Minimum Cost Homomorphism Dichotomy for Oriented Cycles
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Communication: Minimum cost and list homomorphisms to semicomplete digraphs
Discrete Applied Mathematics
Discrete Applied Mathematics
Bounded tree-width and CSP-related problems
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Minimum cost homomorphisms to reflexive digraphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Extensions of the minimum cost homomorphism problem
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Approximation algorithms for graph homomorphism problems
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
Constraint optimization problems and bounded tree-width revisited
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
The maximum solution problem on graphs
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Approximation of minimum cost homomorphisms
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
The complexity of conservative valued CSPs
Journal of the ACM (JACM)
The complexity of three-element min-sol and conservative min-cost-hom
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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Level of repair analysis (LORA) is a prescribed procedure for defense logistics support planning. For a complex engineering system containing perhaps thousands of assemblies, sub-assemblies, components, etc. organized into several levels of indenture and with a number of possible repair decisions, LORA seeks to determine an optimal provision of repair and maintenance facilities to minimize overall life-cycle costs. For a LORA problem with two levels of indenture with three possible repair decisions, which is of interest in UK and US military and which we call LORA-BR, Barros [The optimisation of repair decisions using life-cycle cost parameters. IMA J. Management Math. 9 (1998) 403-413] and Barros and Riley [A combinatorial approach to level of repair analysis, European J. Oper. Res. 129 (2001) 242-251] developed certain branch-and-bound heuristics. The surprising result of this paper is that LORA-BR is, in fact, polynomial-time solvable. To obtain this result, we formulate the general LORA problem as an optimization homomorphism problem on bipartite graphs, and reduce a generalization of LORA-BR, LORA-M, to the maximum weight independent set problem on a bipartite graph. We prove that the general LORA problem is NP-hard by using an important result on list homomorphisms of graphs. We introduce the minimum cost graph homomorphism problem, provide partial results and pose an open problem. Finally, we show that our result for LORA-BR can be applied to prove that an extension of the maximum weight independent set problem on bipartite graphs is polynomial time solvable.