Parallel algorithms for minimum general partial dominating set and maximum budgeted dominating set in unit disk graph

Abstract

In a minimum general partial dominating set problem (MinGPDS), given a graph G=(V,E), a profit function p:V→R+ and a threshold K, the goal is to find a minimum subset of vertices D⊆V such that the total profit of those vertices dominated by D is at least K (a vertex is dominated by D if it is either in D or has at least one neighbor in D). In a maximum general budgeted dominating set problem (MaxGBDS), given a budget B, the goal is to find a vertex set D with at most B vertices such that the total profit of those vertices dominated by D is as large as possible. We present the first parallel algorithms for MinGPDS and MaxGBDS in unit disk graphs. They both run in O(log⁡n) rounds on O(n) machines, and achieve constant approximation ratios.