Random generation of combinatorial structures from a uniform
Theoretical Computer Science
Dualization of regular Boolean functions
Discrete Applied Mathematics
An O(mn) algorithm for regular set-covering problems
Theoretical Computer Science
On generating all maximal independent sets
Information Processing Letters
Complexity of identification and dualization of positive Boolean functions
Information and Computation
Interior and exterior functions of Boolean functions
Discrete Applied Mathematics
On the complexity of dualization of monotone disjunctive normal forms
Journal of Algorithms
Fast discovery of association rules
Advances in knowledge discovery and data mining
On generating the irredundant conjunctive and disjunctive normal forms of monotone Boolean functions
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Inner-core and outer-core functions of partially defined Boolean functions
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Dual-Bounded Generating Problems: Partial and Multiple Transversals of a Hypergraph
SIAM Journal on Computing
Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
On the Complexity of Generating Maximal Frequent and Minimal Infrequent Sets
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Random Walks on Truncated Cubes and Sampling 0-1 Knapsack Solutions
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Enumerating spanning and connected subsets in graphs and matroids
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Computational aspects of monotone dualization: A brief survey
Discrete Applied Mathematics
On the complexity of monotone dualization and generating minimal hypergraph transversals
Discrete Applied Mathematics
Scientific contributions of Leo Khachiyan (a short overview)
Discrete Applied Mathematics
An intersection inequality for discrete distributions and related generation problems
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Some fixed-parameter tractable classes of hypergraph duality and related problems
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Hi-index | 0.00 |
An integral-valued set function f:2v ↦ Z is called polymatroid if it is submodular, nondecreasing, and f(φ) = 0. Given a polymatroid function f and an integer threshold t ≥ 1, let α = α(f,t) denote the number of maximal sets X ⊆ V satisfying f(X) t, let β = β(f,t) be the number of minimal sets X ⊆ V for which f(X) ≥ t, and let n = |V|. We show that if β ≥ 2 then α ≤ β(log t)/c, where c = c(n,β) is the unique positive root of the equation 1 = 2c(nc/log β - 1). In particular, our bound implies that α ≤ (nβ)log t for all β ≥ 1. We also give examples of polymatroid functions with arbitrarily large t, n, α and β for which α ≥ β(0.551 log t)/c. More generally, given a polymatroid function f : 2v ↦ Z and an integral threshold t ≥ 1, consider an arbitrary hypergraph H' such that |H'| ≥ 2 and f(H) ≥ t for all H ∈ H'. Let f' be the family of all maximal independent sets X of H' for which f(X) . Then |f'| ≤ |H'|(log t)/c(n,|H'|). As an application, we show that given a system of polymatroid inequalities f1(X) ≥ t1,..., fm(X) ≥ tm with quasi-polynomially bounded right-hand sides t1,....,tm, all minimal feasible solutions to this system can be generated in incremental quasi-polynomial time. In contrast to this result, the generation of all maximal infeasible sets is an NP-hard problem for many polymatroid inequalities of small range.