# Stas Busygin's Home Page

### Selected writings

- A Least Squares Framework for the Maximum Weight Clique Problem, 2002-2007.
- A New Trust Region Technique for the Maximum Weight Clique Problem,
*Discrete Applied Mathematics 154(15) (International Symposium on Combinatorial Optimization CO'02)*,
pp. 2080-2096, 2006.
- On NP-hardness of the clique partition -- independence number gap recognition and
related problems,
*Discrete Mathematics 304(4)*, pp. 460-463, 2006
(with D.V. Pasechnik, see also ECCC Report TR03-052).
- The SAT01 framework for NP problems, 2003.
- A Simple Clique Camouflaging Against Greedy Maximum Clique Heuristics, 2002.

### Software

- QUALEX-MS: QUick ALmost EXact Maximum Weight
Clique/Independent Set Solver based on the Motzkin-Straus QP formulation.
Here is 80 DIMACS graphs
on which the algorithm was tested.
- theta-weighted-dimacs
computes the (weighted) Lovasz number (theta function) of a graph given in the text or binary
DIMACS format.
- JacMat: Jacobson-Matthews random Latin square generator.
- AntiSM: generator of graphs hard for greedy maximum
clique heuristics (described in this paper.)

### Chess

I am a US National Master in chess.

Stas Busygin <busygin@gmail.com>

Last update 07/23/12