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GD
2009
Springer
14 years 1 months ago
Complexity of Some Geometric and Topological Problems
We show that recognizing intersection graphs of convex sets has the same complexity as deciding truth in the existential theory of the reals. Comparing this to similar results on t...
Marcus Schaefer
CORR
2006
Springer
132views Education» more  CORR 2006»
13 years 10 months ago
The Connectivity of Boolean Satisfiability: Computational and Structural Dichotomies
Boolean satisfiability problems are an important benchmark for questions about complexity, algorithms, heuristics and threshold phenomena. Recent work on heuristics, and the satis...
Parikshit Gopalan, Phokion G. Kolaitis, Elitza N. ...
GD
2007
Springer
14 years 4 months ago
Crossing Number of Graphs with Rotation Systems
We show that computing the crossing number of a graph with a given rotation system is NP-complete. This result leads to a new and much simpler proof of Hlinˇen´y’s result, tha...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...
FOCS
2002
IEEE
14 years 2 months ago
A Dichotomy Theorem for Constraints on a Three-Element Set
The Constraint Satisfaction Problem (CSP) provides a common framework for many combinatorial problems. The general CSP is known to be NP-complete; however, certain restrictions on...
Andrei A. Bulatov
DM
2007
114views more  DM 2007»
13 years 10 months ago
An inequality for the group chromatic number of a graph
—We give an inequality for the group chromatic number of a graph as an extension of Brooks’ Theorem. Moreover, we obtain a structural theorem for graphs satisfying the equality...
Hong-Jian Lai, Xiangwen Li, Gexin Yu