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## Computación y Sistemas

*Print version* ISSN 1405-5546

#### Abstract

ALONSO, Roberto and MONROY, Raúl. **On the NP-Completeness of Computing the Commonality** **Among the Objects Upon Which a Collection of Agents Has Performed an Action**.* Comp. y Sist.* [online]. 2013, vol.17, n.4, pp.489-500.
ISSN 1405-5546.

We prove the NP-completeness of the so-called *Social Group Commonality* (SGC) problem which queries the commonality among the objects 'touched' by collections of agents while executing an action. Although it naturally arises in several contexts, *e.g.,* in profiling the behavior of a collection of system users, SGC (to the authors' knowledge) has 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 which we call *2-SGC,* where the commonality among 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. Finally, we hypothesize that the optimality version of SGC is NP-hard, hinting on how to deal with the proof obligation.

**Keywords
:
**Social Group Commonality; complexity theory; social networks; graphs.