Algorithms to Exploit Data Sparsity

While data in the real world is very high-dimensional, it generally has some underlying structure; for instance, if we think of an image as a set of pixels with associated color values, most possible settings of color values correspond to something more like random noise than what we typically think of as a picture. With an appropriate transformation of basis, this underlying structure can often be converted into sparsity in data, giving an equivalent representation of the data where the magnitude is large in only a few directions relative to the ambient dimension. This motivates a variety of theoretical questions around designing algorithms that can exploit this data sparsity to achieve better performance than what would be possible naively, and in this thesis we tackle several such questions.We first examine the question of simply approximating the level of sparsity of a signal under several different measurement models, a natural first step if the sparsity is to be exploited by other algorithms. Second, we look at a particular sparse signal recovery problem called nonadaptive probabilistic group testing, and investigate the question of exactly how sparse the signal needs to be before the methods used for recovering sparse signals outperform those used for non-sparse signals. Third, we prove novel upper bounds on the number of measurements needed to recover a sparse signal in the universal one-bit compressed sensing model of sparse signal recovery. Fourth, we give some approximations of an information-theoretic quantity called the index coding rate of a network modeled by a graph, in the special case that the graph is sparse or otherwise highly structured. For each of the problems considered, we also discuss some remaining open questions and conjectures, as well as possible directions towards their solutions

Theory Learning with Symmetry Breaking

This paper investigates the use of a Prolog coded SMT solver in tackling a well known constraints problem, namely packing a given set of consecutive squares into a given rectangle, and details the developments in the solver that this motivates. The packing problem has a natural model in the theory of quantifier-free integer difference logic, a theory supported by many SMT solvers. The solver used in this work exploits a data structure consisting of an incremental Floyd-Warshall matrix paired with a watch matrix that monitors the entailment status of integer difference constraints. It is shown how this structure can be used to build unsatisfiable theory cores on the fly, which in turn allows theory learning to be incorporated into the solver. Further, it is shown that a problem-specific and non-standard approach to learning can be taken where symmetry breaking is incorporated into the learning stage, magnifying the effect of learning. It is argued that the declarative framework allows the solver to be used in this white box manner and is a strength of the solver. The approach is experimentally evaluated

Weighted F-free Edge Editing

Ein F-freier Graph besitzt keinen induzierten Teilgraphen aus einer Menge von verbotenen Teilgraphen F. Man kann Kanten in einem Graphen editieren (einfügen oder entfernen) um einen Graphen zu erreichen, der F-frei ist. Das Ziel von F-free Edge Editing ist es, eine minimale Menge an Editierungsoperation zu finden, die zu einem F-freien Graphen führen. Wir betrachten eine Generalisierung, Weighted F-free Edge Editing, die beliebige Kosten für die Editierungsoperationen erlaubt. In dieser Arbeit fokussieren wir uns auf einen parametrisierten Suchbaumalgorithmus (FPT) mit den Editierungskosten als Parameter. Wir adaptieren bereits existierende Beschleunigungstechniken für das ungewichteten Editieren für den gewichteten Fall. Unter anderem betrachten wir Algorithmen zum Berechnen von unteren Schranken und Strategien für die Auswahl von Teilgraphen zum Verzweigen. Außerdem diskutieren wir das Problem, die optimalen Editierungskosten für den Suchbaumalgorithmus zu finden und präsentieren dafür zwei neue Suchstrategien. Zusätzlich behandeln wir einen Algorithmus basierend auf ganzahliger linearer Optimierung (ILP) und Methoden, die die Anzahl der generierten Bedingungen beschränken. Des Weiteren evaluieren wir die FPT und ILP Algorithmen und ihre Beschleunigungstechniken auf Protein-Protein Interaktionsgraphen für F = {C4, P4}. Wir stellen fest, dass der FPT Algorithmus am meisten von dem Greedy-Algorithmus für untere Schranken und der Auswahlstrategie “most adjacent” profitiert. Letztere präferiert Teilgraphen, die zu vielen anderen verbotenen Teilgraphen adjazent sind. Auch fanden wir heraus, dass der Algorithmus für die untere Schranken, der auf lokaler Suche basiert, im gewichteten Fall größere Probleme mit lokalen Maxima hat. Weiterhin bemerken wir, dass das Beschränken der Anzahl der generierten Bedingungen den ILP Algorithmus signifikant schneller werden lässt. Schlussendlich haben wir beide Lösungsalgorithmen verglichen und kamen zum Schluss, dass der ILP Algorithmus konsistent besser ist als der FPT Algorithmus

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

Preemptive mobile code protection using spy agents

This thesis introduces 'spy agents' as a new security paradigm for evaluating trust in remote hosts in mobile code scenarios. In this security paradigm, a spy agent, i.e. a mobile agent which circulates amongst a number of remote hosts, can employ a variety of techniques in order to both appear 'normal' and suggest to a malicious host that it can 'misuse' the agent's data or code without being held accountable. A framework for the operation and deployment of such spy agents is described. Subsequently, a number of aspects of the operation of such agents within this framework are analysed in greater detail. The set of spy agent routes needs to be constructed in a manner that enables hosts to be identified from a set of detectable agent-specific outcomes. The construction of route sets that both reduce the probability of spy agent detection and support identification of the origin of a malicious act is analysed in the context of combinatorial group testing theory. Solutions to the route set design problem are proposed. A number of spy agent application scenarios are introduced and analysed, including: a) the implementation of a mobile code email honeypot system for identifying email privacy infringers, b) the design of sets of agent routes that enable malicious host detection even when hosts collude, and c) the evaluation of the credibility of host classification results in the presence of inconsistent host behaviour. Spy agents can be used in a wide range of applications, and it appears that each application creates challenging new research problems, notably in the design of appropriate agent route sets

Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)

The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..