Journal of Computer and System Sciences
Journal of Algorithms
An application of the Planar Separator Theorem to counting problems
Information Processing Letters
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Easy problems for tree-decomposable graphs
Journal of Algorithms
Probabilistically checkable debate systems and approximation algorithms for PSPACE-hard functions
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Random Debaters and the Hardness of Approximating Stochastic Functions
SIAM Journal on Computing
Semiring-based constraint satisfaction and optimization
Journal of the ACM (JACM)
Closure properties of constraints
Journal of the ACM (JACM)
The Complexity of Planar Counting Problems
SIAM Journal on Computing
Colored Tutte polynomials and Kaufman brackets for graphs of bounded tree width
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
An Algebraic Model for Combinatorial Problems
SIAM Journal on Computing
Dynamic Programming on Graphs with Bounded Treewidth
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
Bounding the Bandwidth of NP-Complete Problems
WG '80 Proceedings of the International Workshop on Graphtheoretic Concepts in Computer Science
Mathematical Structures Underlying Greedy Algorithms
FCT '81 Proceedings of the 1981 International FCT-Conference on Fundamentals of Computation Theory
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Deterministic versus nondeterministic time and lower bound problems
Journal of the ACM (JACM)
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We study the computational problem "find the value of the quantified formula obtained by quantifying the variables in a sum of terms." The "sum" can be based on any commutative monoid, the "quantifiers" need only satisfy two simple conditions, and the variables can have any finite domain. This problem is a generalization of the problem "given a sum-of-products of terms, find the value of the sum" studied in [R.E. Stearns and H.B. Hunt III, SIAM J. Comput. 25 (1996) 448-476]. A data structure called a "structure tree" is defined which displays information about "subproblems" that can be solved independently during the process of evaluating the formula. Some formulas have "good" structure trees which enable certain generic algorithms to evaluate the formulas in significantly less time than by brute force evaluation. By "generic algorithm," we mean an algorithm constructed from uninterpreted function symbols, quantifier symbols, and monoid operations. The algebraic nature of the model facilitates a formal treatment of "local reductions" based on the "local replacement" of terms. Such local reductions "preserve formula structure" in the sense that structure trees with nice properties transform into structure trees with similar properties. These local reductions can also be used to transform hierarchical specified problems with useful structure into hierarchically specified problems having similar structure.