An application of the Planar Separator Theorem to counting problems
Information Processing Letters
Journal of the ACM (JACM)
The Complexity of Planar Counting Problems
SIAM Journal on Computing
SIAM Journal on Computing
Vertex cover: further observations and further improvements
Journal of Algorithms
An algorithm for counting maximum weighted independent sets and its applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Introduction to Algorithms
Combinatorial Approaches to Finding Subtle Signals in DNA Sequences
Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Approximation Algorithms for Some Parameterized Counting Problems
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Efficient Generation of Triconnected Plane Triangulations
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Approximate counting by dynamic programming
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A determinant-based algorithm for counting perfect matchings in a general graph
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The Parameterized Complexity of Counting Problems
SIAM Journal on Computing
List Decoding of Error-Correcting Codes: Winning Thesis of the 2002 ACM Doctoral Dissertation Competition (Lecture Notes in Computer Science)
A faster parameterized algorithm for set packing
Information Processing Letters
Enumerate and expand: new runtime bounds for vertex cover variants
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Efficient algorithms for detecting signaling pathways in protein interaction networks
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
Parameterized Complexity
A Fixed-Parameter Enumeration Algorithm for the Weighted FVS Problem
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
An Efficient Fixed-Parameter Enumeration Algorithm for Weighted Edge Dominating Set
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
The union of minimal hitting sets: Parameterized combinatorial bounds and counting
Journal of Discrete Algorithms
The union of minimal hitting sets: parameterized combinatorial bounds and counting
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
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In the field of computational optimization, it is often the case that we are given an instance of an NP problem and asked to enumerate the first few ”best” solutions to the instance. Motivated by this, we propose in this paper a new framework to measure the effective enumerability of NP optimization problems. More specifically, given an instance of an NP problem, we consider the parameterized problem of enumerating a given number of best solutions to the instance, and study its average complexity in terms of the number of solutions. Our framework is different from the previously-proposed ones. For example, although it is known that counting the number of k-paths in a graph is #W[1]-complete, we present a fixed-parameter enumeration algorithm for the problem. We show that most algorithmic techniques for fixed-parameter tractable problems, such as search trees, color coding, and bounded treewidth, can be used for parameterized enumerations. In addition, we design elegant and new enumeration techniques and show how to generate small-size structures and enumerate solutions efficiently.