Two algorithmic results for the traveling salesman problem
Mathematics of Operations Research
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Parallel Algorithms with Optimal Speedup for Bounded Treewidth
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
NC-Algorithms for Graphs with Small Treewidth
WG '88 Proceedings of the 14th International Workshop on Graph-Theoretic Concepts in Computer Science
Completeness classes in algebra
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Parallel and Distributed Finite Constraint Satisfaction: Complexity, Algorithms and Experiments
Parallel and Distributed Finite Constraint Satisfaction: Complexity, Algorithms and Experiments
Holographic Algorithms (Extended Abstract)
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
The combinatorial approach yields an NC algorithm for computing Pfaffians
Discrete Applied Mathematics
Characterizing valiant's algebraic complexity classes
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
On the Expressive Power of CNF Formulas of Bounded Tree- and Clique-Width
Graph-Theoretic Concepts in Computer Science
Tree-width in Algebraic Complexity
Fundamenta Informaticae - Bridging Logic and Computer Science: to Johann A. Makowsky for his 60th birthday
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
On the expressive power of CNF formulas of bounded tree- and clique-width
Discrete Applied Mathematics
An extended tree-width notion for directed graphs related to the computation of permanents
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Characterizing arithmetic circuit classes by constraint satisfaction problems
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Log-Space Algorithms for Paths and Matchings in k-Trees
Theory of Computing Systems
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Valiant introduced some 25 years ago an algebraic model of computation along with the complexity classes VP and VNP, which can be viewed as analogues of the classical classes P and NP. Prominent examples of difficult (that is, VNP-complete) problems in this model includes the permanent and hamiltonian polynomials. In this paper we investigate the expressive power of easy special cases of these polynomials. We show that the permanent and hamiltonian polynomials for matrices of bounded treewidth both are equivalent to arithmetic formulas. Also, arithmetic weakly skew circuits are shown to be equivalent to the sum of weights of perfect matchings of planar graphs.