On the NP-Completeness of Computing the Commonality Amongst the Objects upon which a Collection of Agents has Performed an Action

Authors

  • Roberto Alonso Instituto Tecnológico y de Estudios Superiores de Monterrey, Campus Estado de México
  • Raúl Monroy Instituto Tecnológico y de Estudios Superiores de Monterrey, Campus Estado de México

DOI:

https://doi.org/10.13053/cys-17-4-1451

Keywords:

Social Group Commonality, complexity theory, LCS, HS, graphs.

Abstract

We prove the NP-completeness of a problem, we call Social Group Commonality (SGC), which queries the commonality amongst the objects ‘touched’ by a collections of agents while executing an action. Although it naturally arises in several contexts, e.g., to profile the behaviour of a collection of system users, SGC has, to the authors’ knowledge, been ignored. Our proof of SGC NP-completeness consists of a Karp reduction, from the well-known Longest Common Subsequence (LCS) problem to SGC. We also prove that a special case of SGC, we call 2-SGC, where the commonality amongst actions is limited to agent pairs, remains NP- complete. For proving NP-completeness of 2-SGC, though, our reduction departs from the well-known Hitting Set problem. Before concluding the paper, we hypothesise that the optimality version of SGC is NP-hard, hinting on how to deal with the proof obligation.

Author Biography

Raúl Monroy, Instituto Tecnológico y de Estudios Superiores de Monterrey, Campus Estado de México

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Published

2013-12-30

Issue

Vol. 17 No. 4 (2013): 17(4) October-December 2013

Section

Articles

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