The classification of coverings of processor networks
Journal of Parallel and Distributed Computing
Computing Boolean functions on anonymous networks
Information and Computation
Computing on Anonymous Networks: Part I-Characterizing the Solvable Cases
IEEE Transactions on Parallel and Distributed Systems
Journal of Combinatorial Theory Series B
Fixed parameter complexity of λ-labelings
Discrete Applied Mathematics - special issue on the 25th international workshop on graph theoretic concepts in computer science (WG'99)
Local and global properties in networks of processors (Extended Abstract)
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Generalized H-coloring and H-covering of trees
Nordic Journal of Computing
Graph Theory With Applications
Graph Theory With Applications
A complete complexity classification of the role assignment problem
Theoretical Computer Science - Graph colorings
Local Computations in Graphs: The Case of Cellular Edge Local Computations
Fundamenta Informaticae - SPECIAL ISSUE ON ICGT 2004
Locally constrained graph homomorphisms and equitable partitions
European Journal of Combinatorics
Complexity of Partial Covers of Graphs
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
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The universal cover TG of a connected graph G is the unique (possible infinite) tree covering G, i.e., that allows a locally bijective homomorphism from TG to G. Universal covers have major applications in the area of distributed computing. It is well-known that if a graph G covers a graph H then their universal covers are isomorphic, and that the latter can be tested in polynomial time by checking if G and H share the same degree refinement matrix. We extend this result to locally injective and locally surjective homomorphisms by following a very different approach. Using linear programming techniques we design two polynomial time algorithms that check if there exists a locally injective or a locally surjective homomorphism, respectively, from a universal cover TG to a universal cover TH. This way we obtain two heuristics for testing the corresponding locally constrained graph homomorphisms. As a consequence, we have obtained a new polynomial time algorithm for testing (subgraph) isomorphism between universal covers, and for checking if there exists a role assignment (locally surjective homomorphism) from a given tree to an arbitrary fixed graph H.