Graph classes: a survey
Algorithms for Vertex Partitioning Problems on Partial k-Trees
SIAM Journal on Discrete Mathematics
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
Worst-case upper bounds for MAX-2-SAT with an application to MAX-CUT
Discrete Applied Mathematics - The renesse issue on satisfiability
Exact (exponential) algorithms for the dominating set problem
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Pathwidth of cubic graphs and exact algorithms
Information Processing Letters
Improved fixed parameter tractable algorithms for two “edge” problems: MAXCUT and MAXDAG
Information Processing Letters
Partial vs. Complete Domination: t-Dominating Set
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
A New Upper Bound for Max-2-SAT: A Graph-Theoretic Approach
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
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
Pathwidth of cubic graphs and exact algorithms
Information Processing Letters
A new upper bound for Max-2-SAT: A graph-theoretic approach
Journal of Discrete Algorithms
A universally fastest algorithm for Max 2-Sat, Max 2-CSP, and everything in between
Journal of Computer and System Sciences
A faster algorithm for the steiner tree problem
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Branching and treewidth based exact algorithms
ISAAC'06 Proceedings of the 17th international conference on Algorithms and 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
Linear-programming design and analysis of fast algorithms for Max 2-CSP
Discrete Optimization
New bounds for MAX-SAT by clause learning
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
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We prove that given a graph, one can efficiently find a set of no more than m/5.217 + 1 nodes whose removal yields a partial two-tree. As an application, we immediately get simple algorithms for several problems, including Max-Cut, Max-2-SAT and Max-2-XSAT. All of these take a record-breaking time of O*(2m/5.217), where m is the number of clauses or edges, while only using polynomial space. Moreover, the existence of the aforementioned node sets implies an upper bound of m/5.217 + 3 on the treewidth of a graph with m edges. Letting go of polynomial space restrictions, this can be improved to a bound of m/5.769 + O(log n) on the pathwidth, leading to algorithms for the above problems that take O*(2m/5.769) time.