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18
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 waking up other robots. The go ..."
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Cited by 32 (6 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...
Minimizing Movement
"... 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 14 (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.
Improved approximation algorithms for the freezetag problem
 In Proceedings of the 15th annual ACM symposium on Parallel algorithms and architectures
, 2003
"... Abstract The following scheduling problem naturally arises in thestudy 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 stand ..."
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Cited by 12 (1 self)
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Abstract The following scheduling problem naturally arises in thestudy 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 otherrobots. 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,
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 10 (2 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
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 8 (1 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.
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 6 (1 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
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 5 (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
Why Robots Need Maps ⋆
"... Abstract. A large group of autonomous, mobile entities e.g. robots initially placed at some arbitrary node of the graph has to jointly visit all nodes (not necessarily all edges) and finally return to the initial position. The graph is not known in advance (an online setting) and robots have to trav ..."
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Cited by 4 (0 self)
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Abstract. A large group of autonomous, mobile entities e.g. robots initially placed at some arbitrary node of the graph has to jointly visit all nodes (not necessarily all edges) and finally return to the initial position. The graph is not known in advance (an online setting) and robots have to traverse an edge in order to discover new parts (edges) of the graph. The team can locally exchange information, using wireless communication devices. We compare cost of the online and optimal offline algorithm which knows the graph beforehand (competitive ratio). If the cost is the total time of exploraiton, we prove the lower bound of Ω(log k / log log k) for competitive ratio of any deterministic algorithm (using global communication). This significantly improves the best known constant lower bound. For the cost being the maximal number of edges traversed by a robot (the energy) we present an improved (4 − 2/k)competitive online algorithm for trees. 1
Minimizing Movement: FixedParameter Tractability
"... Abstract. We study an extensive class of movement minimization problems which arise from many practical scenarios but so far have little theoretical study. In general, these problems involve planning the coordinated motion of a collection of agents (representing robots, people, map labels, network m ..."
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Cited by 4 (2 self)
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Abstract. We study an extensive class of movement minimization problems which arise from many practical scenarios but so far have little theoretical study. In general, these problems involve planning the coordinated motion of a collection of agents (representing robots, people, map labels, network messages, etc.) to achieve a global property in the network while minimizing the maximum or average movement (expended energy). The only previous theoretical results about this class of problems are about approximation, and mainly negative: many movement problems of interest have polynomial inapproximability. Given that the number of mobile agents is typically much smaller than the complexity of the environment, we turn to fixedparameter tractability. We characterize the boundary between tractable and intractable movement problems in a very general set up: it turns out the complexity of the problem fundamentally depends on the treewidth of the minimal configurations. Thus the complexity of a particular problem can be determined by answering a purely combinatorial question. Using our general tools, we determine the complexity of several concrete problems and fortunately show that many movement problems of interest can be solved efficiently. 1
Online Dispersion Algorithms for Swarms of Robots
"... We illustrate algorithms for dispersing a swarm of primitive robots in a twodimensional unknown environment R. Each robot in the swarm is equipped with a very simple sensor that is able to query the contents of neighboring locations to test the presence of other robots or obstacles. Based on the se ..."
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Cited by 1 (0 self)
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We illustrate algorithms for dispersing a swarm of primitive robots in a twodimensional unknown environment R. Each robot in the swarm is equipped with a very simple sensor that is able to query the contents of neighboring locations to test the presence of other robots or obstacles. Based on the sensor readings, at each time step a robot may decide to take a discrete step to a neighboring (grid) point. The objective is to minimize the makespan, that is, the time to fill R with robots, one per grid point inside R. We focus here on the case of a discrete environment, composed of unit squares (pixels) that are induced by the integer grid within a polygonal domain R. There is at most one robot per pixel and robots move horizontally or vertically at unit speed. Robots enter R by means of k ≥ 1 door pixels on the boundary of R, each of which acts as an infinite source of robots. Robots are primitive finite automata, only having local communication, local sensors, and a constantsized memory...