Faster approximation for maximum independent set on unit disk graph

Faster Approximation for Maximum Independent Set on Unit Disk Graph

Maximum independent set from a given set D of unit disks intersecting a horizontal line can be solved in O(n) time and O(n) space. As a corollary, we design a factor 2 approximation algorithm for the maximum independent set problem on unit disk graph which takes both time and space of O(n). The best known factor 2 approximation algorithm for this problem runs in O(n logn) time and takes O(n) sp...

Approximation algorithms for maximum independent set of a unit disk graph

We propose a 2-approximation algorithm for the maximum independent set problem for a unit disk graph. The time and space complexities are O(n) and O(n), respectively. For a penny graph, our proposed 2-approximation algorithm works in O(n logn) time using O(n) space. We also propose a polynomial-time approximation scheme (PTAS) for the maximum independent set problem for a unit disk graph. Given...

Approximation Algorithms for Maximum Independent Set Problems and Fractional Coloring Problems on Unit Disk Graphs

Unit disk graphs are the intersection graphs of equal sized circles in the plane. In this paper, we consider the maximum independent set problems on unit disk graphs. When the given unit disk graph is de ned on a slab whose width is k, we propose an algorithm for nding a maximum independent set in O(n 4 d 2k= p 3 e ) time where n denotes the number of vertices. We also propose a (1 1=r)-approxi...

Report On the Approximation of Unit Disk Graph Coordinates

In this paper we study a problem occuring in the context of geometric routing algorithms for mobile ad-hoc networks: Finding unit disk graph coordinates given a graph G = (V, E). Based on a proof that recognition of unit disk graphs is an NP-hard problem, we show that the problem of finding unit disk graph coordinates given a graph G = (V, E) is NPhard. Subsequently, we show that the proof does...

Approximation Algorithms for Maximum Cliques in 3D Unit-Disk Graphs