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1| {#1 |}% {G}% % % H% H% {V}% 1#1% {E}% {E}% R R X r 1#1 q 1V #1 P 1 #1 {m} 2\!#1 ({#2) } polylog N Z p 2\| {#1 - #2 \|} q s For an undirected graph G= (V, E), with n vertices and m edges, the densest subgraph problem, is to compute a subset S V which maximizes the ratio |ES| / |S|, where ES E is the set of all edges of G with endpoints in S. The densest subgraph problem is a well studied problem in computer science. Existing exact and approximation algorithms for computing the densest subgraph require (m) time. We present near-linear time (in n) approximation algorithms for the densest subgraph problem on implicit geometric intersection graphs, where the vertices are explicitly given but not the edges. As a concrete example, we consider n disks in the plane with arbitrary radii and present two different approximation algorithms.
Har-Peled et al. (Tue,) studied this question.