Dieter Mitsche

On the satisfiability threshold of formulas with three literals per clause

In this paper we present a new upper bound for randomly chosen 3-CNF formulas. In particular we show that any random formula over n variables, with a clauses-to-variables ratio of at least 4.4898 is, as n grows large, asymptotically almost surely unsatisfiable. The previous best such bound, due to Dubois in 1999, was 4.506. The first such bound, independently discovered by many groups of researchers since 1983, was 5.19. Several decreasing values between 5.19 and 4.506 were published in the years between. We believe that the probabilistic techniques we use for the proof are of independent interest.

Large Connectivity for Dynamic Random Geometric Graphs

We provide the first rigorous analytical results for the connectivity of dynamic random geometric graphs - a model for mobile wireless networks in which vertices move in random directions in the unit torus. The model presented here follows the one described. We provide precise asymptotic results for the expected length of the connectivity and disconnectivity periods of the network. We believe that the formal tools developed in this work could be extended to be used in more concrete settings and in more realistic models, in the same manner as the development of the connectivity threshold for static random geometric graphs has affected a lot of research done on ad hoc networks.

Reconstructing many partitions using spectral techniques

A partitioning of a set of n items is a grouping of these items into k disjoint, equally sized classes. Any partition can be modeled as a graph. The items become the vertices of the graph and two vertices are connected by an edge if and only if the associated items belong to the same class. In a planted partition model a graph that models a partition is given, which is obscured by random noise, i.e., edges within a class can get removed and edges between classes can get inserted. The task is to reconstruct the planted partition from this graph. In the model that we study the number k of classes controls the difficulty of the task. We design a spectral partitioning algorithm that asymptotically almost surely reconstructs up to

A new upper bound for 3-SAT ∗

k = c\sqrt{n}

Sharp Threshold for Hamiltonicity of Random Geometric Graphs

partitions, where c is a small constant, in time Ck poly(n), where C is another constant.

The random waypoint mobility model with uniform node spatial distribution

We show that a randomly chosen 3-CNF formula over n variables with clauses-to- variables ratio at least 4.4898 is asymptotically almost surely unsatisfiable. The previous best such bound, due to Dubois in 1999, was 4.506. The first such bound, independently discovered by many groups of researchers since 1983, was 5.19. Several decreasing values between 5.19 and 4.506 were published in the years between. The probabilistic techniques we use for the proof are, we believe, of independent interest.

Off-line admission control for advance reservations in star networks

We show for an arbitrary

The Robber Strikes Back

\ell_p

Social-aware forwarding improves routing performance in pocket switched networks

norm that the property that a random geometric graph

ON THE RELATION BETWEEN GRAPH DISTANCE AND EUCLIDEAN DISTANCE IN RANDOM GEOMETRIC GRAPHS

\mathcal G(n,r)