On the evaluation at (3,3) of the Tutte polynomial of a graph
Journal of Combinatorial Theory Series B
Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
The complexity of counting graph homomorphisms
Proceedings of the ninth international conference on on Random structures and algorithms
The Complexity of Counting in Sparse, Regular, and Planar Graphs
SIAM Journal on Computing
Quantum Circuits That Can Be Simulated Classically in Polynomial Time
SIAM Journal on Computing
Theoretical Computer Science
The Computational Complexity of Tutte Invariants for Planar Graphs
SIAM Journal on Computing
The complexity of partition functions
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Towards a dichotomy theorem for the counting constraint satisfaction problem
Information and Computation
SIAM Journal on Computing
On the Theory of Matchgate Computations
Theory of Computing Systems
Holant problems and counting CSP
Proceedings of the forty-first annual ACM symposium on Theory of computing
The complexity of weighted Boolean #CSP with mixed signs
Theoretical Computer Science
The Complexity of Weighted Boolean CSP
SIAM Journal on Computing
On Symmetric Signatures in Holographic Algorithms
Theory of Computing Systems - Special Issue: Theoretical Aspects of Computer Science; Guest Editors: Wolgang Thomas and Pascal Weil
Graph homomorphisms with complex values: a dichotomy theorem
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Holographic algorithms: From art to science
Journal of Computer and System Sciences
Holographic Algorithms with Matchgates Capture Precisely Tractable Planar_#CSP
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
A Complexity Dichotomy for Partition Functions with Mixed Signs
SIAM Journal on Computing
Dichotomy theorems for holant problems
Dichotomy theorems for holant problems
Computational Complexity of Holant Problems
SIAM Journal on Computing
Gadgets and anti-gadgets leading to a complexity dichotomy
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
A Dichotomy for Real Weighted Holant Problems
CCC '12 Proceedings of the 2012 IEEE Conference on Computational Complexity (CCC)
Spin systems on k-regular graphs with complex edge functions
Theoretical Computer Science
A complete dichotomy rises from the capture of vanishing signatures: extended abstract
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
| Hi-index | 0.00 |
We prove a complexity dichotomy theorem for symmetric complex-weighted Boolean #CSP when the constraint graph of the input must be planar. The problems that are #P-hard over general graphs but tractable over planar graphs are precisely those with a holographic reduction to matchgates. This generalizes a theorem of Cai, Lu, and Xia for the case of real weights. We also obtain a dichotomy theorem for a symmetric arity 4 signature with complex weights in the planar Holant framework, which we use in the proof of our #CSP dichotomy. In particular, we reduce the problem of evaluating the Tutte polynomial of a planar graph at the point (3,3) to counting the number of Eulerian orientations over planar 4-regular graphs to show the latter is #P-hard. This strengthens a theorem by Huang and Lu to the planar setting.