Improved Algorithm for Maximum Independent Set on Unit Disk Graph

Faster approximation for maximum independent set on unit disk graph

“…• We design a factor 2 approximation algorithm for MISUDG problem which takes both O(n 2 ) time and space. It is an improvement over the best known result on this problem proposed by Jallu et al [1]. They gave a factor 2 approximation algorithm for this problem where the time and space complexities are O(n 2 log n) and O(n 2 ) respectively.…”

“…For a given positive integer k > 1, they gave a (1 + 1 k ) 2 factor approximation algorithm which runs in O(k 4 n σ k log k + n log n) time and O(n + k log k) space, where σ k ≤ 7k 3 + 2. Recently, Jallu and Das [1], improved the running time of the same problem to n O(k) by keeping the approximation factor same. A fixed parameter tractable algorithm for the MISUDG problem was proposed by van Leeuwen [14].…”

“…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 2 ). The best known factor 2 approximation algorithm for this problem runs in O(n 2 log n) time and takes O(n 2 ) space [1,2].…”

The Generalized Independent and Dominating Set Problems on Unit Disk Graphs

“…The MIS problem is well studied on UDGs too and is shown to be NP-hard [9]. Unlike in general graphs, the problem admits approximation algorithms [31,23,33,11,28,37] and approximation schemes [13,39,11,28].…”