Exact Algorithms for Maximum Clique: a computational study
نویسنده
چکیده
We investigate a number of recently reported exact algorithms for the maximum clique problem. The program code is presented and analyzed to show how small changes in implementation can have a drastic effect on performance. The computational study demonstrates how problem features and hardware platforms influence algorithm behaviour. The effect of vertex ordering is investigated. One of the algorithms (MCS) is broken into its constituent parts and we discover that one of these parts frequently degrades performance. It is shown that the standard procedure used for rescaling published results (i.e., adjusting run times based on the calibration of a standard program over a set of benchmarks) is unsafe and can lead to incorrect conclusions being drawn from empirical data.
منابع مشابه
A new exact algorithm for the maximum-weight clique problem based on a heuristic vertex-coloring and a backtrack search
In this paper we present an exact algorithm for the maximum-weight clique problem on arbitrary undirected graphs. The algorithm based on a fact that vertices from the same independent set couldn’t be included into the same maximum clique. Those independent sets are obtained from a heuristic vertex coloring where each of them is a color class. Color classes and a backtrack search are used for pr...
متن کاملClique, independent set, and graph coloring
This article introduces the closely related maximum clique, maximum independent set, graph coloring, and minimum clique partitioning problems. The survey includes some of the most important results concerning these problems, including their computational complexity, known bounds, mathematical programming formulations, and exact and heuristic algorithms to solve them.
متن کاملPolyhedral study of the maximum common induced subgraph problem
In this paper we present an exact algorithm for the Maximum Common Induced Subgraph Problem (MCIS) by addressing it directly, using Integer Programming (IP) and polyhedral combinatorics. We study the MCIS polytope and introduce strong valid inequalities, some of which we prove to define facets. Besides, we show an equivalence between our IP model for MCIS and a well-known formulation for the Ma...
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 کاملA Branch and Bound Algorithm for Matching Protein Structures
An efficient branch and bound algorithm for matching protein structures has been developed. The compared protein structures are represented as graphs and a product graph of these graphs is calculated. The resulting product graph is then the input to our algorithm. A maximum clique in the product graph corresponds to the maximum common substructure in the original graphs. Our algorithm, which gi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Algorithms
دوره 5 شماره
صفحات -
تاریخ انتشار 2012