The Anonymous Subgraph Problem

Authors:
Andrea Bettinelli;Leo Liberti;Franco Raimondi;David Savourey
Affiliations:
DTI, Universití degli Studi di Milano, Via Bramante 65, 26013 Crema (CR), Italy;LIX, ícole Polytechnique, F-91128 Palaiseau, France;School of Science and Technology, Middlesex University, London, UK;LIX, ícole Polytechnique, F-91128 Palaiseau, France
Venue:
Computers and Operations Research
Year:
2013

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Abstract

In this work we address the Anonymous Subgraph Problem (ASP). The problem asks to decide whether a directed graph contains anonymous subgraphs of a given family. This problem has a number of practical applications and here we describe three of them (Secret Santa Problem, anonymous routing, robust paths) that can be formulated as ASPs. Our main contributions are (i) a formalization of the anonymity property for a generic family of subgraphs, (ii) an algorithm to solve the ASP in time polynomial in the size of the graph under a set of conditions, and (iii) a thorough evaluation of our algorithms using various tests based both on randomly generated graphs and on real-world instances.