Finding Small Complete Subgraphs Efficiently

Dumitrescu, Adrian; Lingas, Andrzej

doi:10.1007/978-3-031-34347-6_16

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2024

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“…The problem is also studied in other models of computation, including parallel and data streaming [9][10][11][12]. See also [13][14][15] for some recent work on the related triangle detection problem.…”

Section: Related Workmentioning

confidence: 99%

On the Maximum Triangle Problem

Jabal Ameli,

Zarrabi-Zadeh

2024

Scientia Iranica

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Given a set P of n points in the plane, the maximum triangle problem asks for finding a triangle with three vertices in P that encloses the maximum number of points from P . While the problem is easily solvable in O(n 3 ) time, it has been open whether a subcubic solution is possible. In this paper, we show that the problem can be solved in o(n 3 ) time, using a reduction to min-plus matrix multiplication. We also provide some improved approximation algorithms for the problem, including a 4-approximation algorithm running in O(n log n log h) time, and a 3-approximation algorithm with O(nh log n + nh 2 ) runtime, where h is the size of the convex hull of P .

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