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*Nonnumerical* *Algorithms* and Problems—geometrical

"... Topology control in ad-hoc networks tries to lower node energy consumption by reducing transmission power and by confining interference, collisions and consequently retransmissions. Commonly low interference is claimed to be a consequence to sparseness of the resulting topology. In this paper we dis ..."

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topology control

*algorithms*do not effectively constrain interference. Furthermore we propose connectivity-preserving and spanner constructions that are interference-minimal.###
*Nonnumerical* *Algorithms* and Problems—geometrical

"... All too often a seemingly insurmountable divide between theory and practice can be witnessed. In this paper we try to contribute to narrowing this gap in the field of ad-hoc routing. In particular we consider two aspects: We propose a new geometric routing algorithm which is outstandingly efficient ..."

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All too often a seemingly insurmountable divide between theory and practice can be witnessed. In this paper we try to contribute to narrowing this gap in the field of ad-hoc routing. In particular we consider two aspects: We propose a new geometric routing

*algorithm*which is outstandingly efficient###
*Nonnumerical* *Algorithms* and Problems—Computations

"... While the evolution of biological networks can be modeled sensefully as a series of mutation and selection, evolution of other networks such as the social network in a city or the network of streets in a country is not determined by selection since there is no alternative network with which these si ..."

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While the evolution of biological networks can be modeled sensefully as a series of mutation and selection, evolution of other networks such as the social network in a city or the network of streets in a country is not determined by selection since there is no alternative network with which these singular networks have to compete. Nonetheless, these singular networks do evolve due to dynamic changes of vertices and edges. In this article we present a formal, analyzable framework for the evolution of singular networks. We show that the careful design of adaptation rules can lead to the emergence of network topologies with satisfying performance in polynomial time while other adaptation rules yield exponential runtime. We further show by example how the framework could be applied to some ad-hoc communication scenarios.

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*Nonnumerical* *Algorithms* and Problems—[Geometrical

"... The main result of this paper is an extension of de Silva’s Weak Delaunay Theorem to smoothly embedded curves and surfaces in Euclidean space. Assuming a sufficiently fine sampling, we prove that i + 1 points in the sample span an i-simplex in the restricted Delaunay triangulation iff every subset o ..."

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The main result of this paper is an extension of de Silva’s Weak Delaunay Theorem to smoothly embedded curves and surfaces in Euclidean space. Assuming a sufficiently fine sampling, we prove that i + 1 points in the sample span an i-simplex in the restricted Delaunay triangulation iff every subset of the i + 1 points has a weak witness.

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*Nonnumerical* *Algorithms* and Problems—Computations

"... Persistent homology captures the topology of a filtration – a one-parameter family of increasing spaces – in terms of a complete discrete invariant. This invariant is a multiset of intervals that denote the lifetimes of the topological entities within the filtration. In many applications of topology ..."

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Persistent homology captures the topology of a filtration – a one-parameter family of increasing spaces – in terms of a complete discrete invariant. This invariant is a multiset of intervals that denote the lifetimes of the topological entities within the filtration. In many applications of topology, we need to study a multifiltration: a family of spaces parameterized along multiple geometric dimensions. In this paper, we show that no similar complete discrete invariant exists for multidimensional persistence. Instead, we propose the rank invariant, a discrete invariant for the robust estimation of Betti numbers in a multifiltration, and prove its completeness in one dimension.

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*Nonnumerical* *Algorithms* and Problems—computations

"... A Bloom filter is a probabilistic bit-array-based set representation that has recently been applied to address-set disambiguation in systems that ease the burden of parallel programming. However, many of these systems intersect the Bloom filter bit-arrays to approximate address-set intersection and ..."

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A Bloom filter is a probabilistic bit-array-based set representation that has recently been applied to address-set disambiguation in systems that ease the burden of parallel programming. However, many of these systems intersect the Bloom filter bit-arrays to approximate address-set intersection and decide set disjointness. This is in contrast with the conventional and well-studied approach of making individual membership queries into the Bloom filter. In this paper we present much-needed probabilistic models for the unconventional application of testing set disjointness using Bloom filters. Consequently, we demonstrate that intersecting Bloom filters requires substantially larger bit-arrays to provide the same probability of false set-overlap as querying into the bit-array. For when intersection is unavoidable, we prove that partitioned Bloom filters require less space than unpartitioned. Finally, we show that for Bloom filters with a single hash function, surprisingly, intersection and querying share the same probability of false set-overlap.

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*Nonnumerical* *Algorithms* and Problems

"... We study a simple game-theoretic model for the spread of an innovation in a network. The diffusion of the innovation is modeled as the dynamics of a coordination game in which the adoption of a common strategy between players has a higher payoff. Classical results in game theory provide a simple con ..."

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We study a simple game-theoretic model for the spread of an innovation in a network. The diffusion of the innovation is modeled as the dynamics of a coordination game in which the adoption of a common strategy between players has a higher payoff. Classical results in game theory provide a simple condition for the innovation to spread through the network. The present paper characterizes the rate of convergence as a function of graph structure. In particular, we derive a dichotomy between well-connected (e.g. random) graphs that show slow convergence and poorly connected, low dimensional graphs that show fast convergence.

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*Algorithms* and Problem Complexity]: *Nonnumerical* *Algorithms*

"... Moving point object data can be analyzed through the discovery of patterns. We consider the computational efficiency of computing two of the most basic spatio-temporal patterns in trajectories, namely flocks and meetings. The patterns are large enough subgroups of the moving point objects that exhib ..."

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that exhibit similar movement and proximity for a certain amount of time. We consider the problem of computing a longest duration flock or meeting. We give several exact and approximation

*algorithms*, and also show that some variants are as hard as MaxClique to compute and approximate.###
and Problem Complexity—*Nonnumerical* *Algorithms* and Problems

"... We describe an algorithm for Byzantine agreement that is scalable in the sense that each processor sends only Õ( √ n) bits, where n is the total number of processors. Our algorithm succeeds with high probability against an adaptive adversary, which can take over processors at any time during the pro ..."

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We describe an

*algorithm*for Byzantine agreement that is scalable in the sense that each processor sends only Õ( √ n) bits, where n is the total number of processors. Our*algorithm*succeeds with high probability against an adaptive adversary, which can take over processors at any time during