An O(20.304n) Algorithm for Solving Maximum Independent Set Problem
IEEE Transactions on Computers
A lower bound for DLL algorithms for k-SAT (preliminary version)
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
New upper bounds for maximum satisfiability
Journal of Algorithms
Improved algorithms for 3-coloring, 3-edge-coloring, and constraint satisfaction
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A deterministic (2 - 2/(k+ 1))n algorithm for k-SAT based on local search
Theoretical Computer Science
3-coloring in time 0(1.3446^n): a no-MIS algorithm
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
An Improved Exponential-Time Algorithm for k-SAT
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
A Probabilistic Algorithm for k-SAT and Constraint Satisfaction Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
Improved upper bounds for 3-SAT
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Quasiconvex analysis of backtracking algorithms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Exact (exponential) algorithms for the dominating set problem
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Enumerating maximal independent sets with applications to graph colouring
Operations Research Letters
Parameterized Complexity
Measure and conquer: a simple O(20.288n) independent set algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Pathwidth of cubic graphs and exact algorithms
Information Processing Letters
An improved exact algorithm for the domatic number problem
Information Processing Letters
Faster Steiner Tree Computation in Polynomial-Space
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Combinatorial bounds via measure and conquer: Bounding minimal dominating sets and applications
ACM Transactions on Algorithms (TALG)
ACM SIGACT News
A universally fastest algorithm for Max 2-Sat, Max 2-CSP, and everything in between
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
On Independent Sets and Bicliques in Graphs
Graph-Theoretic Concepts in Computer Science
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Improved edge-coloring with three colors
Theoretical Computer Science
Exponential time algorithms for the minimum dominating set problem on some graph classes
ACM Transactions on Algorithms (TALG)
Exact Algorithms for Dominating Clique Problems
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
On Partitioning a Graph into Two Connected Subgraphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Exact algorithms for maximum acyclic subgraph on a superclass of cubic graphs
WALCOM'08 Proceedings of the 2nd international conference on Algorithms and computation
Exact algorithms for edge domination
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
A moderately exponential time algorithm for full degree spanning tree
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
A hybrid graph representation for recursive backtracking algorithms
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Exact and parameterized algorithms for edge dominating set in 3-degree graphs
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
An exact algorithm for connected red-blue dominating set
Journal of Discrete Algorithms
Fast exact algorithm for L(2, 1)-labeling of graphs
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
ACM Transactions on Algorithms (TALG)
Algorithms and constraint programming
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
A branch-and-reduce algorithm for finding a minimum independent dominating set in graphs
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Improved edge-coloring with three colors
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Solving connected dominating set faster than 2n
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
A faster algorithm for the steiner tree problem
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Exponential time algorithms for the minimum dominating set problem on some graph classes
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Exact computation of maximum induced forest
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Nonblocker: parameterized algorithmics for minimum dominating set
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
Bounding the number of minimal dominating sets: a measure and conquer approach
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Parameterized algorithms for HITTING SET: the weighted case
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
An exact algorithm for the minimum dominating clique problem
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Exact algorithms for finding the minimum independent dominating set in graphs
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Intuitive algorithms and t-vertex cover
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Counting independent sets in claw-free graphs
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
A faster algorithm for dominating set analyzed by the potential method
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Improved worst-case complexity for the MIN 3-SET COVERING problem
Operations Research Letters
A refined exact algorithm for edge dominating set
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Exact algorithms for L(2, 1)-labeling of graphs
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Counting minimum weighted dominating sets
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Hi-index | 0.00 |
Davis-Putnam-style exponential-time backtracking algorithms are the most common algorithms used for finding exact solutions of NP-hard problems. The analysis of such recursive algorithms is based on the bounded search tree technique: a measure of the size of the subproblems is defined; this measure is used to lower bound the progress made by the algorithm at each branching step. For the last 30 years the research on exact algorithms has been mainly focused on the design of more and more sophisticated algorithms. However, measures used in the analysis of backtracking algorithms are usually very simple. In this paper we stress that a more careful choice of the measure can lead to significantly better worst case time analysis. As an example, we consider the minimum dominating set problem. The currently fastest algorithm for this problem has running time O(20.850n) on n-nodes graphs. By measuring the progress of the (same) algorithm in a different way, we refine the time bound to O(20.598 n). A good choice of the measure can provide such a (surprisingly big) improvement; this suggests that the running time of many other exponential-time recursive algorithms is largely overestimated because of a “bad” choice of the measure.