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32
The FreezeTag Problem: How to Wake Up a Swarm of Robots
 In Proc. 13th ACMSIAM Sympos. Discrete Algorithms
, 2002
"... An optimization problem that naturally arises in the study of "swarm robotics" is to wake up a set of "asleep" robots, starting with only one "awake" robot. One robot can only awaken another when they are in the same location. As soon as a robot is awake, it assists in ..."
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Cited by 31 (4 self)
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An optimization problem that naturally arises in the study of "swarm robotics" is to wake up a set of "asleep" robots, starting with only one "awake" robot. One robot can only awaken another when they are in the same location. As soon as a robot is awake, it assists in waking up other robots. The goal is to compute an optimal awakening schedule such that all robots are awake by time t , for the smallest possible value of t . We consider both scenarios on graphs and in geometric environments. In the graph setting, robots sleep at vertices and there is a length function on the edges. An awake robot can travel from vertex to vertex along edges, and the length of an edge determines the time it takes to travel from one vertex to the other. While this problem bears some resemblance to problems from various areas in combinatorial optimization such as routing, broadcasting, scheduling and covering, its algorithmic characteristics are surprisingly different. We prove that the problem is NPhard, even for the special case of star graphs. We also establish hardness of approximation, showing that it is NPhard to obtain an approximation factor better than 5/3, even for graphs of bounded degree. These lower bounds are complemented with several algorithmic results. We present a simple online algorithm that is O(log)competitive for graphs with maximum degree . Other results include algorithms that require substantially more sophistication and development of new techniques: (1) The natural greedy strategy on star graphs has a worstcase performance of 7/3, which is tight. (2) There exists a PTAS for star graphs. (3) For the problem Dept. of Appl. Math. and Statistics, SUNY Stony Brook, NY 117943600, festie, jsbmg@ams.sunysb.edu. y Dept. of Computer Science, SUNY St...
Controlling swarms of robots using interpolated implicit functions
 in Proc. IEEE Int. Conf. Robot. Autom., 2005
"... ©2005 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other wo ..."
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Cited by 30 (7 self)
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©2005 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This paper is posted at ScholarlyCommons.
Minimizing Movement
, 2007
"... We give approximation algorithms and inapproximability results for a class of movement problems. In general, these problems involve planning the coordinated motion of a large collection of objects (representing anything from a robot swarm or firefighter team to map labels or network messages) to ach ..."
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Cited by 18 (2 self)
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We give approximation algorithms and inapproximability results for a class of movement problems. In general, these problems involve planning the coordinated motion of a large collection of objects (representing anything from a robot swarm or firefighter team to map labels or network messages) to achieve a global property of the network while minimizing the maximum or average movement. In particular, we consider the goals of achieving connectivity (undirected and directed), achieving connectivity between a given pair of vertices, achieving independence (a dispersion problem), and achieving a perfect matching (with applications to multicasting). This general family of movement problems encompass an intriguing range of graph and geometric algorithms, with several realworld applications and a surprising range of approximability. In some cases, we obtain tight approximation and inapproximability results using direct techniques (without use of PCP), assuming just that P != NP.
Robotic swarm dispersion using wireless intensity signals
 in Proc. Int’l Symp. on Distributed Autonomous Robotic Systems
, 2006
"... Summary. Dispersing swarms of robots to cover an unknown, potentially hostile area is useful to setup a sensor network for surveillance. Previous research assumes relative locations (distance and bearing) of neighboring robots are available to each robot through sensors. Many robots are too small to ..."
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Cited by 18 (3 self)
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Summary. Dispersing swarms of robots to cover an unknown, potentially hostile area is useful to setup a sensor network for surveillance. Previous research assumes relative locations (distance and bearing) of neighboring robots are available to each robot through sensors. Many robots are too small to carry sensors capable of providing this information. We use wireless signal intensity as a rough approximation of distance to assist a large swarm of small robots in dispersion. Simulation experiments indicate that a swarm can effectively disperse through the use of wireless signal intensities without knowing the relative locations of neighboring robots. 1
Dispersing robots in an unknown environment
 in 7th International Symposium on Distributed Autonomous Robotic Systems (DARS
, 2004
"... Summary. We examine how the choice of the movement algorithm can affect the success of a swarm of simple mobile robots attempting to disperse themselves in an unknown environment. We assume there is no central control, and the robots have limited processing power, simple sensors, and no active commu ..."
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Cited by 13 (1 self)
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Summary. We examine how the choice of the movement algorithm can affect the success of a swarm of simple mobile robots attempting to disperse themselves in an unknown environment. We assume there is no central control, and the robots have limited processing power, simple sensors, and no active communication. We evaluate different movement algorithms based on the percentage of the environment that the group of robots succeeds in observing. 1
Improved approximation algorithms for the freezetag problem
 IN PROCEEDINGS OF THE 15TH ANNUAL ACM SYMPOSIUM ON PARALLEL ALGORITHMS AND ARCHITECTURES
, 2003
"... The following scheduling problem naturally arises in the study of swarm robotics. Consider a set of n robots, modeled as points in some metric space (e.g., vertices of an edgeweighted graph). Initially, there is one awake oractive robot and all other robots are asleep, that is, in a standby mode. ..."
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Cited by 12 (1 self)
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The following scheduling problem naturally arises in the study of swarm robotics. Consider a set of n robots, modeled as points in some metric space (e.g., vertices of an edgeweighted graph). Initially, there is one awake oractive robot and all other robots are asleep, that is, in a standby mode. Our objective is to "wake up" all ofthe robots as quickly as possible. In order for an active robot to awaken a sleeping robot, the awake robotmust travel to the location of the slumbering robot. Once awake, this new robot is available to assist in rousing other robots. The objective is to minimize the makespan, that is, the time when the last robot awakens. This problemis the FreezeTag Problem (FTP) because it resembles the child's game of freezetag. The FTP is a scheduling problem that arises naturallyas a hybrid of problems from the areas of broadcasting,
A MultiAgent Simulation for Assessing Massive Sensor Deployment
 JOURNAL OF BATTLEFIELD TECHNOLOGY
, 2004
"... We present the design and implementation of a multiagent simulation that models deployment and coverage of sensors performing collaborative target detection. The focus is on sensor networks with enough sensors that humans cannot individually manage each. Experiments evaluated both known and novel d ..."
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Cited by 11 (3 self)
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We present the design and implementation of a multiagent simulation that models deployment and coverage of sensors performing collaborative target detection. The focus is on sensor networks with enough sensors that humans cannot individually manage each. Experiments evaluated both known and novel deployment algorithms, and considered effects of the sensor type, number of sensors deployed, presence of obstacles, and mobility of the sensors. A particular focus was barrier (traversal) coverage which has many military applications but which has been less studied than other sensor placement problems; experiments showed that good algorithms for it are different than those good for area monitoring. This work provides both useful data for guiding sensor deployment and a valuable testbed for planning of sensor networks.
From Balls and Bins to Points and Vertices
 ALGORITHMIC OPERATIONS RESEARCH VOL.4 (2009) 133–143
, 2009
"... Given a graph G = (V,E) with V  = n, we consider the following problem. Place m = n points on the vertices of G independently and uniformly at random. Once the points are placed, relocate them using a bijection from the points to the vertices that minimizes the maximum distance between the random ..."
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Cited by 10 (1 self)
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Given a graph G = (V,E) with V  = n, we consider the following problem. Place m = n points on the vertices of G independently and uniformly at random. Once the points are placed, relocate them using a bijection from the points to the vertices that minimizes the maximum distance between the random place of the points and their target vertices.We look for an upper bound on this maximum relocation distance that holds with high probability (over the initial placements of the points). For general graphs and in the case m ≤ n, we prove the #Phardness of the problem and that the maximum relocation distance is O( n) with high probability. We present a Fully Polynomial Randomized Approximation Scheme when the input graph admits a polynomialsize family of witness cuts while for trees we provide a 2approximation algorithm. Many applications concern the variation in which m = (1 − ǫ)n for some 0 < ǫ < 1. We provide several bounds for the maximum relocation distance according to different graph topologies.
Minimizing movement in mobile facility location problems
 In FOCS 2008
"... In the mobile facility location problem, which is a variant of the classical facility location and kmedian problems, each facility and client is assigned to a start location in a metric graph and our goal is to find a destination node for each client and facility such that every client is sent to a ..."
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Cited by 9 (0 self)
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In the mobile facility location problem, which is a variant of the classical facility location and kmedian problems, each facility and client is assigned to a start location in a metric graph and our goal is to find a destination node for each client and facility such that every client is sent to a node which is the destination of some facility. The quality of a solution can be measured either by the total distance clients and facilities travel or by the maximum distance traveled by any client or facility. As we show in this paper (by an approximation preserving reduction), the problem of minimizing the total movement of facilities and clients generalizes the classical kmedian problem. The class of movement problems was introduced by Demaine et al. in SODA 2007 [8], where it was observed q simple 2approximation for the minimum maximum movement mobile facility location while an approximation for the minimum total movement variant and hardness results for both were left as open problems. Our main result here is an 8approximation algorithm for the minimum total movement mobile facility location problem. Our algorithm is obtained by rounding an LP relaxation in five phases. For the minimum maximum movement mobile facility location problem, we show that we cannot have a better than a 2approximation for the problem, unless P = NP; so the simple algorithm observed in [8] is essentially best possible. 1
MultiRobot MultiTarget Particle Swarm Optimization Search in Noisy Wireless Environments
 In Proceedings of the 2nd IEEE Conference on Human System Interaction (HSI 2009
, 2009
"... Multiple small robots (swarms) can work together using Particle Swarm Optimization (PSO) to perform tasks that are difficult or impossible for a single robot to accomplish. The problem considered in this paper is exploration of an unknown environment with the goal of finding a target(s) at an unknow ..."
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Cited by 7 (0 self)
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Multiple small robots (swarms) can work together using Particle Swarm Optimization (PSO) to perform tasks that are difficult or impossible for a single robot to accomplish. The problem considered in this paper is exploration of an unknown environment with the goal of finding a target(s) at an unknown location(s) using multiple small mobile robots. This work demonstrates the use of a distributed PSO algorithm with a novel adaptive RSS weighting factor to guide robots for locating target(s) in high risk environments. The approach was developed and analyzed on multiple robot single and multiple target search. The approach was further enhanced by the multirobotmultitarget search in noisy environments. The experimental results demonstrated how the availability of radio frequency signal can significantly affect robot search time to reach a target. Keywords—fitness, Particle Swarm Optimization (PSO), Received Signal Strength (RSS), wireless I.