Exact Algorithms for Maximum Independent Set
نویسندگان
چکیده
We show that the maximum independent set problem (MIS) on an n-vertex graph can be solved in 1.1996n time and polynomial space, which even is faster than Robson’s 1.2109n-time exponential-space algorithm published in 1986. We also obtain improved algorithms for MIS in graphs with maximum degree 6 and 7, which run in time of 1.1893n and 1.1970n, respectively. Our algorithms are obtained by using fast algorithms for MIS in low-degree graphs in a hierarchical way and making a careful analyses on the structure of bounded-degree graphs.
منابع مشابه
Using Combinatorics to Prune Search Trees: Independent and Dominating Set
We introduce a surprisingly simple technique to design and analyze algorithms based on search trees, that significantly improves many existing results in the area of exact algorithms. The technique is based on measuring the progress of Branch & Bound algorithms by making use of a combinatorial relation between the average and maximum dual degrees of a graph. By dual degree of a vertex, we mean ...
متن کاملAn exact algorithm exhibiting RS-RSB/easy-hard correspondence for the maximum independent set problem
A recently proposed exact algorithm for the maximum independent set problem is analyzed. The typical running time is improved exponentially in some parameter regions compared to simple binary search. The algorithm also overcomes the core transition point, where the conventional leaf removal algorithm fails, and works up to the replica symmetry breaking (RSB) transition point. This suggests that...
متن کاملDistributed algorithms for weighted problems in sparse graphs
We study distributed algorithms for three graph-theoretic problems in weighted trees and weighted planar graphs. For trees, we present an efficient deterministic distributed algorithm which finds an almost exact approximation of a maximum-weight matching. In addition, in the case of trees, we show how to approximately solve the minimum-weight dominating set problem. For planar graphs, we presen...
متن کاملA refined algorithm for maximum independent set in degree-4 graphs
The maximum independent set problem is one of the most important problems in worstcase analysis for exact algorithms. Improvement on this problem in low-degree graphs can be used to get improvement on the problem in general graphs. In this paper, we show that the maximum independent set problem in an n-vertex graph with degree bounded by 4 can be solved in O∗(1.1376n) time and polynomial space,...
متن کاملAn Exact Algorithm for Maximum Independent Set in Degree-5 Graphs
The maximum independent set problem is a basic NP-hard problem and has been extensively studied in exact algorithms. The maximum independent set problems in low-degree graphs are also important and may be bottlenecks of the problem in general graphs. In this paper, we present an O∗(1.1737n)-time exact algorithm for the maximum independent set problem in an n-vertex graph with degree bounded by ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013