An algorithm for counting maximum weighted independent sets and its applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Counting Satisfying Assignments in 2-SAT and 3-SAT
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The complexity of counting self-avoiding walks in subgraphs of two-dimensional grids and hypercubes
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SIGACT News complexity theory column 41
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Algorithms for four variants of the exact satisfiability problem
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The complexity of mining maximal frequent itemsets and maximal frequent patterns
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Counting models for 2SAT and 3SAT formulae
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Computational aspects of mining maximal frequent patterns
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Simple deterministic approximation algorithms for counting matchings
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Holographic algorithms: from art to science
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Fast exponential-time algorithms for the forest counting in graph classes
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Predecessor existence problems for finite discrete dynamical systems
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Counting the number of independent sets in chordal graphs
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Power and stability in connectivity games
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Exact Max 2-Sat: Easier and Faster
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Algorithms for Counting 2-Sat Solutions and Colorings with Applications
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Monotone DNF Formula That Has a Minimal or Maximal Number of Satisfying Assignments
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Sampling Eulerian orientations of triangular lattice graphs
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Holant problems and counting CSP
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A Computational Proof of Complexity of Some Restricted Counting Problems
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Classification of a Class of Counting Problems Using Holographic Reductions
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Maximum edge-disjoint paths problem in planar graphs
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A worst-case time upper bound for counting the number of independent sets
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Holographic reduction: a domain changed application and its partial converse theorems
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Holographic algorithms: From art to science
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On the optimal approximation of queries using tractable propositional languages
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Approximate counting for complex-weighted Boolean constraint satisfaction problems
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A computational proof of complexity of some restricted counting problems
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A novel method for counting models on grid Boolean formulas
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Holographic reduction for some counting problems
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Maximal matching and path matching counting in polynomial time for graphs of bounded clique width
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Closest pair and the post office problem for stochastic points
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Guest column: complexity dichotomies of counting problems
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#3-Regular bipartite planar vertex cover is #p-complete
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Some results on matchgates and holographic algorithms
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Linear-time counting algorithms for independent sets in chordal graphs
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A dichotomy for k-regular graphs with {0, 1}-vertex assignments and real edge functions
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Counting independent sets in claw-free graphs
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Counting maximal independent sets in subcubic graphs
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An exact exponential time algorithm for counting bipartite cliques
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Spin systems on k-regular graphs with complex edge functions
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Planarity, determinants, permanents, and (unique) matchings
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A randomized approximation algorithm for parameterized 3-D matching counting problem
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Weighted counting of k-matchings is #w[1]-hard
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Proof systems and transformation games
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A complete dichotomy rises from the capture of vanishing signatures: extended abstract
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Partition functions on k-regular graphs with {0,1}-vertex assignments and real edge functions
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The complexity of planar boolean #CSP with complex weights
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The complexity of the counting constraint satisfaction problem
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The complexity of complex weighted Boolean #CSP
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Computing cooperative solution concepts in coalitional skill games
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Closest pair and the post office problem for stochastic points
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Sharing rewards in cooperative connectivity games
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Anytime approximation in probabilistic databases
The VLDB Journal — The International Journal on Very Large Data Bases
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We show that a number of graph-theoretic counting problems remain ${\cal NP}$-hard, indeed $\#{\cal P}$-complete, in very restricted classes of graphs. In particular, we prove that the problems of counting matchings, vertex covers, independent sets, and extremal variants of these all remain hard when restricted to planar bipartite graphs of bounded degree or regular graphs of constant degree. We obtain corollaries about counting cliques in restricted classes of graphs and counting satisfying assignments to restricted classes of monotone 2-CNF formulae. To achieve these results, a new interpolation-based reduction technique which preserves properties such as constant degree is introduced.