On the complexity of H-coloring
Journal of Combinatorial Theory Series B
Characterization of the homomorphic preimages of certain oriented cycles
SIAM Journal on Discrete Mathematics
Complexity of tree homomorphisms
Discrete Applied Mathematics
Approximation results for the optimum cost chromatic partition problem
Journal of Algorithms
The Approximability of Constraint Satisfaction Problems
SIAM Journal on Computing
Classification of Homomorphisms to Oriented Cycles and of k-Partite Satisfiability
SIAM Journal on Discrete Mathematics
Homomorphisms to powers of digraphs
Discrete Mathematics - Algebraic and topological methods in graph theory
The Optimal Cost Chromatic Partition Problem for Trees and Interval Graphs
WG '96 Proceedings of the 22nd International Workshop on Graph-Theoretic Concepts in Computer Science
Independent sets of maximum weight in (p,q)-colorable graphs
Discrete Mathematics
Digraph matrix partitions and trigraph homomorphisms
Discrete Applied Mathematics
A dichotomy for minimum cost graph homomorphisms
European Journal of Combinatorics
Coloring of trees with minimum sum of colors
Journal of Graph Theory
Bi-arc graphs and the complexity of list homomorphisms
Journal of Graph Theory
Interval bigraphs and circular arc graphs
Journal of Graph Theory
Communication: Minimum cost homomorphisms to semicomplete multipartite digraphs
Discrete Applied Mathematics
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
A maximal tractable class of soft constraints
Journal of Artificial Intelligence Research
Communication: Level of repair analysis and minimum cost homomorphisms of graphs
Discrete Applied Mathematics
Communication: 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
Minimum Cost Homomorphism Dichotomy for Locally In-Semicomplete Digraphs
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Discrete Applied Mathematics
Minimum cost homomorphisms to oriented cycles with some loops
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
Extensions of the minimum cost homomorphism problem
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
Approximation of minimum cost homomorphisms
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Finding small separators in linear time via treewidth reduction
ACM Transactions on Algorithms (TALG)
Hi-index | 0.01 |
For a fixed digraph H, the minimum cost homomorphism problem, MinHOM(H), asks whether an input digraph G, with given costs ci(u), u ∈ V(G), i ∈ V(H), and an integer k, admits a homomorphism to H of total cost not exceeding k. Minimum cost homomorphism problems encompass many well studied optimization problems such as list homomorphism problems, retraction and precolouring extension problems, chromatic partition optimization, and applied problems in repair analysis. For undirected graphs the complexity of the problem, as a function of the parameter H, is well understood; for digraphs, the situation appears to be more complex, and only partial results are known. We focus on the minimum cost homomorphism problem for reflexive digraphs H. It is known that MinHOM(H) is polynomial if H has a Min-Max ordering. We prove that for any other reflexive digraph H, the problem MinHOM(H) is NP-complete. (This was earlier conjectured by Gutin and Kim.) Apart from undirected graphs, this is the first general class of digraphs for which such a dichotomy has been proved. Our proof involves a forbidden induced subgraph characterization of reflexive digraphs with a Min-Max ordering, and implies a polynomial test for the existence of a Min-Max ordering in a reflexive digraph H.