An O(20.304n) Algorithm for Solving Maximum Independent Set Problem
IEEE Transactions on Computers
Expected computation time for Hamiltonian path problem
SIAM Journal on Computing
On generating all maximal independent sets
Information Processing Letters
Inclusion and exclusion algorithm for the Hamiltonian Path Problem
Information Processing Letters
Number of models and satisfiability of sets of clauses
Theoretical Computer Science
Improved algorithms for 3-coloring, 3-edge-coloring, and constraint satisfaction
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Deciding 3-Colourability in Less Than O(1.415^n) Steps
WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
Solving 3-Satisfiability in Less Then 1, 579n Steps
CSL '92 Selected Papers from the Workshop on Computer Science Logic
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
FOCS '97 Proceedings of the 38th 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
Locally consistent constraint satisfaction problems
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Complexity analysis of a decentralised graph colouring algorithm
Information Processing Letters
The time complexity of constraint satisfaction
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Exact algorithms for exact satisfiability and number of perfect matchings
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Locally consistent constraint satisfaction problems with binary constraints
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Partitioning based algorithms for some colouring problems
CSCLP'05 Proceedings of the 2005 Joint ERCIM/CoLogNET international conference on Constraint Solving and Constraint Logic Programming
Algorithms for the maximum hamming distance problem
CSCLP'04 Proceedings of the 2004 joint ERCIM/CoLOGNET international conference on Recent Advances in Constraints
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We consider worst case time bounds for certain NP-complete problems. In particular, we consider the (k, 2)-satisfiability problem which includes as special cases some canonical problems such as graph coloring and satisfiability. For the (k, 2)-satisfiability problem, we present a randomized algorithm that runs in time O*((k!)n/k)2. This bound is equivalent to O((k/ck)n) with ck increasing to the asymptotic limit e. For k ≥ 11, we improve upon the O((0.4518k)n) randomized bound of Eppstein [Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 329-337]. A special case of (k, 2)- satisfiability is k-colorability; here we achieve the above time bound for a slightly larger ck that has the same asymptotic behavior.