On the Optimality of Spiral Search

Langetepe, Elmar

doi:10.1137/1.9781611973075.1

Cited by 33 publications

(26 citation statements)

References 19 publications

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“…In [10] the authors concentrated on game-theoretic aspects of the situation where multiple selfish pursuers compete to find a target, e.g., in a ring. The main result of [7] is an optimal algorithm to sweep a plane in order to locate an unknown fixed target, where locating means to get the agent originating at point O to a point P such that the target is in the segment OP . In [5] the authors consider the generalization of the search problem in the plane to the case of several searchers.…”

Section: Introductionmentioning

confidence: 99%

Reaching a target in the plane with no information

Pełc

2018

Information Processing Letters

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A mobile agent has to reach a target in the Euclidean plane. Both the agent and the target are modeled as points. At the beginning, the agent is at distance at most D > 0 from the target. Reaching the target means that the agent gets at a sensing distance at most r > 0 from it. The agent has a measure of length and a compass. We consider two scenarios: in the static scenario the target is inert, and in the dynamic scenario it may move arbitrarily at any (possibly varying) speed bounded by v. The agent has no information about the parameters of the problem, in particular it does not know D, r or v. The goal is to reach the target at lowest possible cost, measured by the total length of the trajectory of the agent.Our main result is establishing the minimum cost (up to multiplicative constants) of reaching the target under both scenarios, and providing the optimal algorithm for the agent. For the static scenario the minimum cost is Θ((log D + log 1 r )D 2 /r), and for the dynamic scenario it is Θ((log M + log 1 r )M 2 /r), where M = max (D, v). Under the latter scenario, the speed of the agent in our algorithm grows exponentially with time, and we prove that for an agent whose speed grows only polynomially with time, this cost is impossible to achieve.

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Section: Introductionmentioning

confidence: 99%

Reaching a target in the plane with no information

Pełc

2018

Information Processing Letters

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“…We believe that similar techniques can be applied to many other optimization problems for which doubling algorithms are known to perform well (see, e.g., the survey of Chrobak & Mathieu, 2006). A recent example can be found in the work of Langetepe (2010), concerning the optimality of spiral search for locating a target on the plane.…”

Section: Resultsmentioning

confidence: 99%

Optimal Scheduling of Contract Algorithms for Anytime Problem-Solving

López-Ortíz¹,

Angelopoulos²,

Hamel³

2014

jair

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A contract algorithm is an algorithm which is given, as part of the input, a specified amount of allowable computation time. The algorithm must then complete its execution within the allotted time. An interruptible algorithm, in contrast, can be interrupted at an arbitrary point in time, at which point it must report its currently best solution. It is known that contract algorithms can simulate interruptible algorithms using iterative deepening techniques. This simulation is done at a penalty in the performance of the solution, as measured by the so-called acceleration ratio.In this paper we give matching (i.e., optimal) upper and lower bounds for the acceleration ratio under such a simulation. We assume the most general setting in which n problem instances must be solved by means of scheduling executions of contract algorithms in m identical parallel processors. This resolves an open conjecture of Bernstein, Finkelstein, and Zilberstein who gave an optimal schedule under the restricted setting of round robin and length-increasing schedules, but whose optimality in the general unrestricted case remained open.Lastly, we show how to evaluate the average acceleration ratio of the class of exponential strategies in the setting of n problem instances and m parallel processors. This is a broad class of schedules that tend to be either optimal or near-optimal, for several variants of the basic problem.

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“…A variant of this question is the cow-path problem in [3], in which the searcher has more than two directions to follow. The original problem was also extended to searching in the plane [4], and numerous other variations [12,15,20,22,28,29,31,32,34]. Bose et al [11] recently studied a variant of these problems where upper and lower bounds on the distance to the target are given.…”

Section: Previous Workmentioning

confidence: 99%

Linear Search by a Pair of Distinct-Speed Robots

Bampas¹,

Czyzowicz²,

Gąsieniec³

et al. 2016

Structural Information and Communication Complexity

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Two mobile robots are initially placed at the same point on an infinite line. Each robot may move on the line in either direction not exceeding its maximal speed. The robots need to find a stationary target placed at an unknown location on the line. The search is completed when both robots arrive at the target point. The target is discovered at the moment when either robot arrives at its position. The robot knowing the placement of the target may communicate it to the other robot. We look 123Algorithmica for the algorithm with the shortest possible search time (i.e. the worst-case time at which both robots meet at the target) measured as a function of the target distance from the origin (i.e. the time required to travel directly from the starting point to the target at unit velocity). We consider two standard models of communication between the robots, namely wireless communication and communication by meeting. In the case of communication by meeting, a robot learns about the target while sharing the same location with a robot possessing this knowledge. We propose here an optimal search strategy for two robots including the respective lower bound argument, for the full spectrum of their maximal speeds. This extends the main result of Chrobak et al. (in: Italiano, Margaria-Steffen, Pokorný, Quisquater, Wattenhofer (eds) Current trends in theory and practice of computer science, SOFSEM, 2015) referring to the exact complexity of the problem for the case when the speed of the slower robot is at least one third of the faster one. In the wireless communication model, a message sent by one robot is instantly received by the other robot, regardless of their current positions on the line. For this model, we design a strategy which is optimal whenever the faster robot is at most √ 17 + 4 ≈ 8.123 times faster than the slower one. We also prove that otherwise the wireless communication offers no advantage over communication by meeting.

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On the Optimality of Spiral Search

Cited by 33 publications

References 19 publications

Reaching a target in the plane with no information

Reaching a target in the plane with no information

Optimal Scheduling of Contract Algorithms for Anytime Problem-Solving

Linear Search by a Pair of Distinct-Speed Robots

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