Hypertree decompositions and tractable queries
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
On Tractable Queries and Constraints
DEXA '99 Proceedings of the 10th International Conference on Database and Expert Systems Applications
Reducing Redundancy in the Hypertree Decomposition Scheme
ICTAI '03 Proceedings of the 15th IEEE International Conference on Tools with Artificial Intelligence
Algorithm Design
Constraint solving via fractional edge covers
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Weighted hypertree decompositions and optimal query plans
Journal of Computer and System Sciences
Hypertree width and related hypergraph invariants
European Journal of Combinatorics
A backtracking-based algorithm for hypertree decomposition
Journal of Experimental Algorithmics (JEA)
Heuristic Methods for Hypertree Decomposition
MICAI '08 Proceedings of the 7th Mexican International Conference on Artificial Intelligence: Advances in Artificial Intelligence
Generalized hypertree decompositions: NP-hardness and tractable variants
Journal of the ACM (JACM)
A comparison of structural CSP decomposition methods
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Hi-index | 0.00 |
We propose a greedy algorithm which, given a hypergraph H and a positive integer k, produces a hypertree decomposition of width less than or equal to 3k -- 1, or determines that H does not have a generalized hypertree-width less than k. The running time of this algorithm is O(mk+2n), where m is the number of hyperedges and n is the number of vertices. If k is a constant, it is polynomial. The concepts of (generalized) hypertree decomposition and (generalized) hypertree-width were introduced by Gottlob et al. Many important NP-complete problems in database theory or artificial intelligence are polynomially solvable for classes of instances associated with hypergraphs of bounded hypertree-width. Gottlob et al. also developed a polynomial time algorithm det-k-decomp which, given a hypergraph H and a constant k, computes a hypertree decomposition of width less than or equal to k if the hypertree-width of H is less than or equal to k. The running time of det-k-decomp is O(m2kn2) in the worst case, where m and n are the number of hyperedges and the number of vertices, respectively. The proposed algorithm is faster than this. The key step of our algorithm is checking whether a set of hyperedges is an obstacle to a hypergraph having low generalized hypertree-width. We call such a local hyper-graph structure a k-hyperconnected set. If a hypergraph contains a k-hyperconnected set with a size of at least 2k, it has hypertree-width of at least k. Adler et al. propose another obstacle called a k-hyperlinked set. We discuss the difference between the two concepts with examples.