Hard graphs for the maximum clique problem
نویسندگان
چکیده
منابع مشابه
Hard graphs for the maximum clique problem
The maximum clique problem is one of the NP-complete problems. There are graphs for which a reduction technique exists that transforms the problem for these graphs into one for graphs with specific properties in polynomial time. The resulting graphs do not grow exponentially in order and number. Graphs that allow such a reduction technique are called soft. Hard graphs are those graphs for which...
متن کاملThe maximum clique problem
In this paper we present a survey of results concerning algorithms, complexity, and applications of the maximum clique problem. We discuss enumerative and exact algorithms, heuristics, and a variety of other proposed methods. An up to date bibliography on the maximum clique and related problems is also provided.
متن کاملThe Maximum Clique Problem
Description Given an undirected graph G = ( V, E ), a clique S is a subset of V such that for any two elements u, v ∈ S, ( u, v ) ∈ E. Using the notation ES to represent the subset of edges which have both endpoints in clique S, the induced graph GS = ( S, ES ) is complete. Finding the largest clique in a graph is an NP-hard problem, called the maximum clique problem (MCP). Cliques are intimate...
متن کاملFast Solving Maximum Weight Clique Problem in Massive Graphs
This paper explores techniques for fast solving the maximum weight clique problem (MWCP) in very large scale real-world graphs. Because of the size of such graphs and the intractability of MWCP, previously developed algorithms may not be applicable. Although recent heuristic algorithms make progress in solving MWCP in massive graphs, they still need considerable time to get a good solution. In ...
متن کاملPolyhedral methods for the maximum clique problem
This paper presents an integer programming approach to the maximum clique problem. An initial linear programming relaxation is solved and, when there is an integrality gap, this relaxation is strengthened using one of several tightening procedures. This is done through the addition of cutting planes to the linear program. The bulk of the paper deals with theoretical and computational issues ass...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1988
ISSN: 0012-365X
DOI: 10.1016/0012-365x(88)90207-5