Optimal low-degree hardness of maximum independent set

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.

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...

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

Maximum independent set of rectangles

We study the Maximum Independent Set of Rectangles (MISR) problem: given a collection R of n axis-parallel rectangles, find a maximum-cardinality subset of disjoint rectangles. MISR is a special case of the classical Maximum Independent Set problem, where the input is restricted to intersection graphs of axis-parallel rectangles. Due to its many applications, ranging from map labeling to data m...

Further Improvement on Maximum Independent Set in Graphs with Maximum Degree 4

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∗(1.1446n) time and improves all previous algorithms for this problem. The algorithm is analyzed by using the “Measure and Conquer” method. We use some good reduction and branching rules with a new idea on setting weights to obtain the improved time bound without i...