Confining sets and avoiding bottleneck cases: A simple maximum independent set algorithm in degree-3 graphs

Confining sets and avoiding bottleneck cases: A simple maximum independent set algorithm in degree-3 graphs

We present an O∗(1.0836n)-time algorithm for finding a maximum independent set in an n-vertex graph with degree bounded by 3, which improves all previous running time bounds for this problem. Our approach has the following two features. Without increasing the number of reduction/branching rules to get an improved time bound, we first successfully extract the essence from the previously known re...

Faster computation of maximum independent set and parameterized vertex cover for graphs with maximum degree 3

Further Improvement on Maximum Independent Set in Degree-4 Graphs

We present a simple algorithm for the maximum independent set problem in an n-vertex graph with degree bounded by 4, which runs in O∗(1.1455n) time and improves all previous algorithms for this problem. In this paper, we use the “Measure and Conquer method” to analyze the running time bound, and use some good reduction and branching rules with a new idea on setting weights to obtain the improve...

A 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,...

An Optimal Algorithm to Find Maximum Independent Set and Maximum 2-Independent Set on Cactus Graphs

A cactus graph is a connected graph in which every block is either an edge or a cycle. An optimal algorithm is presented here to find a maximum independent set and maximum 2-independent set on cactus graphs in O(n) time, where n is the total number of vertices of the graph. The cactus graph has many applications in real life problems, specially in radio communication system.