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Convergence speed in distributed consensus and averaging
 IN PROC. OF THE 45TH IEEE CDC
, 2006
"... We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove ..."
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Cited by 52 (1 self)
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We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove lower bounds on the worstcase convergence time for various classes of linear, timeinvariant, distributed consensus methods, and provide an algorithm that essentially matches those lower bounds. We then consider the case of a timevarying topology, and provide a polynomialtime averaging algorithm.
THE TOTAL sENERGY OF A MULTIAGENT SYSTEM
 SIAM J. CONTROL OPTIM, VOL. 49, NO. 4, PP. 1680–1706
, 2011
"... We introduce the total senergy of a multiagent system with timedependent links. This provides a new analytical perspective on bidirectional agreement dynamics, which we use to bound the convergence rates of dynamical systems for synchronization, flocking, opinion dynamics, and social epistemology ..."
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Cited by 5 (4 self)
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We introduce the total senergy of a multiagent system with timedependent links. This provides a new analytical perspective on bidirectional agreement dynamics, which we use to bound the convergence rates of dynamical systems for synchronization, flocking, opinion dynamics, and social epistemology.
Planning Motion in Environments with Similar Obstacles
"... Abstract — In this work, we investigate solutions to the following question: Given two motion planning problems W1 and W2 with the same robot and similar obstacles, can we reuse the computation from W1 to solve W2 more efficiently? While the answer to this question can find many practical applicatio ..."
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Cited by 5 (0 self)
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Abstract — In this work, we investigate solutions to the following question: Given two motion planning problems W1 and W2 with the same robot and similar obstacles, can we reuse the computation from W1 to solve W2 more efficiently? While the answer to this question can find many practical applications, all current motion planners ignore the correspondences between similar environments. Our study shows that by carefully storing and reusing the computation we can gain significant efficiency. I.
A Tight Runtime Bound for Synchronous Gathering of Autonomous Robots with Limited Visibility ∗
"... The problem of gathering n autonomous robots in the Euclidean plane at one (not predefined) point is wellstudied under various restrictions on the capabilities of the robots and in several time models. However, only very few runtime bounds are known. We consider the scenario of local algorithms in ..."
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Cited by 4 (0 self)
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The problem of gathering n autonomous robots in the Euclidean plane at one (not predefined) point is wellstudied under various restrictions on the capabilities of the robots and in several time models. However, only very few runtime bounds are known. We consider the scenario of local algorithms in which the robots can only observe their environment within a fixed viewing range and have to base their decision where to move in the next step solely on the relative positions of the robots within their viewing range. Such local algorithms have to guarantee that the (initially connected) unit disk graph defined by the viewing range of the robots stays connected at all times. In this paper, we focus on the synchronous setting in which all robots are activated concurrently.
Physarum Can Compute Shortest Paths
"... Physarum Polycephalum is a slime mold that apparently is able to solve shortest path problems. A mathematical model has been proposed by biologists to describe the feedback mechanism used by the slime mold to adapt its tubular channelswhileforaging twofood sourcess0 ands1. Weprove that, under this m ..."
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Cited by 2 (0 self)
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Physarum Polycephalum is a slime mold that apparently is able to solve shortest path problems. A mathematical model has been proposed by biologists to describe the feedback mechanism used by the slime mold to adapt its tubular channelswhileforaging twofood sourcess0 ands1. Weprove that, under this model, the mass of the mold will eventually converge to the shortest s0s1 path of the network that the mold lies on, independently of the structure of the network or of the initial mass distribution. This matches the experimental observations by the biologists and can be seen as an example of a “natural algorithm”, that is, an algorithm developed by evolution over millions of years.
Collaborative Search on the Plane Without Communication
 In Proceedings of the 31st ACM Symposium on Principles of Distributed Computing (PODC
, 2012
"... We use distributed computing tools to provide a new perspective on the behavior of cooperative biological ensembles. We introduce the Ants Nearby Treasure Search (ANTS) problem, a generalization of the classical cowpath problem [10, 20, 41, 42], which is relevant for collective foraging in animal g ..."
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Cited by 2 (0 self)
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We use distributed computing tools to provide a new perspective on the behavior of cooperative biological ensembles. We introduce the Ants Nearby Treasure Search (ANTS) problem, a generalization of the classical cowpath problem [10, 20, 41, 42], which is relevant for collective foraging in animal groups. In the ANTS problem, k identical (probabilistic) agents, initially placed at some central location, collectively search for a treasure in the twodimensional plane. The treasure is placed at a target location by an adversary and the goal is to find it as fast as possible as a function of both k and D, where D is the distance between the central location and the target. This is biologically motivated by cooperative, central place foraging, such as performed by ants around their nest. In this type of search there is a strong preference to locate nearby food sources before those that are further away. We focus on trying to find what can be achieved if communication is limited or altogether absent. Indeed, to avoid overlaps agents must be highly dispersed making communication difficult. Furthermore, if the agents do not commence the search in synchrony, then even initial communication is problematic. This holds, in particular, with respect to the question
Selfimproving Algorithms for Convex Hulls
, 2009
"... We give an algorithm for computing planar convex hulls in the selfimproving model: given a sequence I1, I2,... of planar npoint sets, the upper convex hull conv(I) of each set I is desired. We assume that there exists a probability distribution D on npoint sets, such that the inputs Ij are drawn ..."
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Cited by 2 (2 self)
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We give an algorithm for computing planar convex hulls in the selfimproving model: given a sequence I1, I2,... of planar npoint sets, the upper convex hull conv(I) of each set I is desired. We assume that there exists a probability distribution D on npoint sets, such that the inputs Ij are drawn independently according to D. Furthermore, D is such that the individual points are distributed independently of each other. In other words, the i’th point is distributed according to Di. The Di’s can be arbitrary but are independent of each other. The distribution D is not known to the algorithm in advance. After a learning phase of nε rounds, the expected time to compute conv(I) is O(n + H(conv(I))). Here, H(conv(I)) is the entropy of the output, which is a lower bound for the expected running time of any algebraic computation tree that computes the convex hull. (More precisely, H(conv(I)) is the minimum entropy of any random variable that maps I to a description of conv(I) and to a labeling scheme that proves nonextremality for every point in I not on the hull.) Our algorithm is thus asymptotically optimal for D. 1
Triangulating the Square and Squaring the Triangle: Quadtrees and Delaunay Triangulations Are Equivalent
, 2011
"... We show that Delaunay triangulations and compressed quadtrees are equivalent structures. More precisely, we give two algorithms: the first computes a compressed quadtree for a planar point set, given the Delaunay triangulation; the second finds the Delaunay triangulation, given a compressed quadtree ..."
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Cited by 2 (1 self)
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We show that Delaunay triangulations and compressed quadtrees are equivalent structures. More precisely, we give two algorithms: the first computes a compressed quadtree for a planar point set, given the Delaunay triangulation; the second finds the Delaunay triangulation, given a compressed quadtree. Both algorithms run in deterministic linear time on a pointer machine. Our work builds on and extends previous results by Krznaric and Levcopolous [40] and Buchin and Mulzer [10]. Our main tool for the second algorithm is the wellseparated pair decomposition (WSPD) [13], a structure that has been used previously to find Euclidean minimum spanning trees in higher dimensions [27]. We show that knowing the WSPD (and a quadtree) suffices to compute a planar EMST in linear time. With the EMST at hand, we can find the Delaunay triangulation in linear time [21]. As a corollary, we obtain deterministic versions of many previous algorithms related to Delaunay triangulations, such as splitting planar Delaunay triangulations [19, 20], preprocessing imprecise points for faster Delaunay computation [9, 42], and transdichotomous Delaunay triangulations [10, 15, 16].
Direction Election in Flocking Swarms ∗
"... Swarm gathering and swarm flocking may conflict each other. Without explicit communication, such conflicts may lead to undesired topological changes since there is no global signal that facilitates coordinated and safe switching from one behavior to the other. Moreover, without coordination signals ..."
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Cited by 1 (1 self)
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Swarm gathering and swarm flocking may conflict each other. Without explicit communication, such conflicts may lead to undesired topological changes since there is no global signal that facilitates coordinated and safe switching from one behavior to the other. Moreover, without coordination signals multiple swarm members might simultaneously assume leadership, and their conflicting leading direction is likely to nullify a successful flocking effort. To the best of our knowledge, we present the first set of swarm flocking algorithms that maintain connectivity while electing direction for flocking. The algorithms allow spontaneous direction requests and support direction changes.
Distributed Load Balancing for Parallel Agentbased Simulations
"... Abstract—We focus on agentbased simulations where a large number of agents move in the space, obeying to some simple rules. Since such kind of simulations are computational intensive, it is challenging, for such a contest, to let the number of agents to grow and to increase the quality of the simul ..."
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Cited by 1 (0 self)
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Abstract—We focus on agentbased simulations where a large number of agents move in the space, obeying to some simple rules. Since such kind of simulations are computational intensive, it is challenging, for such a contest, to let the number of agents to grow and to increase the quality of the simulation. A fascinating way to answer to this need is by exploiting parallel architectures. In this paper, we present a novel distributed load balancing schema for a parallel implementation of such simulations. The purpose of such schema is to achieve an high scalability. Our approach to load balancing is designed to be lightweight and totally distributed: the calculations for the balancing take place at each computational step, and influences the successive step. To the best of our knowledge, our approach is the first distributed load balancing schema in this context. We present both the design and the implementation that allowed us to perform a number of experiments, with upto 1,000,000 agents. Tests show that, in spite of the fact that the load balancing algorithm is local, the workload distribution is balanced while the communication overhead is negligible.