Optimal Exploration of Terrains with Obstacles

Czyzowicz, Jurek; Ilcinkas, David; Labourel, Arnaud; Pełc, Andrzej

doi:10.1007/978-3-642-13731-0_1

Cited by 5 publications

(8 citation statements)

References 19 publications

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“…A similar setting is considered in [1], in which each agent has to return regularly to the starting point, for example for refueling. Online exploration of polygons is considered in [3,12].…”

Section: Related Workmentioning

confidence: 99%

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Fast collaborative graph exploration

Dereniowski

Disser

Kosowski

et al. 2015

Information and Computation

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We study the following scenario of online graph exploration. A team of k agents is initially located at a distinguished vertex r of an undirected graph. At every time step, each agent can traverse an edge of the graph. All vertices have unique identifiers, and upon entering a vertex, an agent obtains the list of identifiers of all its neighbors. We ask how many time steps are required to complete exploration, i.e., to make sure that every vertex has been visited by some agent.We consider two communication models: one in which all agents have global knowledge of the state of the exploration, and one in which agents may only exchange information when simultaneously located at the same vertex. As our main result, we provide the first strategy which performs exploration of a graph with n vertices at a distance of at most D from r in time O(D), using a team of agents of polynomial size k = Dn 1+ < n 2+ , for any > 0. Our strategy works in the local communication model, without knowledge of global parameters such as n or D.We also obtain almost-tight bounds on the asymptotic relation between exploration time and team size, for large k.

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Section: Related Workmentioning

confidence: 99%

“…Let s be the first step in which all vertices are visited when executing S in T . By (3) and by the choice of T ,…”

Section: Lower Boundsmentioning

confidence: 99%

Fast collaborative graph exploration

Dereniowski

Disser

Kosowski

et al. 2015

Information and Computation

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“…One can show that the minimum length of a watchman tour for a polygon P with h holes is O(per(P ) + √ h · diam(P )), and this bound is tight for polygons P with per(P ) > c · diam(P ), for any fixed c > 2; see [10,14] for two different proofs. Dumitrescu and Tóth [14] show how to find a tour of length O(per(P )+ √ h·diam(P )) in time O(n log n) and also provide related results for polyhedra with holes in 3-space.…”

Section: Prior and Relatedmentioning

confidence: 96%

Approximating Watchman Routes

Mitchell

2013

Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms

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Given a connected polygonal domain P , the watchman route problem is to compute a shortest path or tour for a mobile guard (the "watchman") that is required to see every point of P . While the watchman route problem is polynomially solvable in simple polygons, it is known to be NP-hard in polygons with holes.We present the first polynomial-time approximation algorithm for the watchman route problem in polygonal domains.Our algorithm has an approximation factor O(log 2 n). Further, we prove that the problem cannot be approximated in polynomial time to within a factor of c log n, for a constant c > 0, assuming that P =NP. IntroductionA classic problem in computational geometry is the watchman route problem (WRP): Compute a shortest path/tour within a polygonal domain (polygon with holes) P so that every point of P is seen from some point of the path/tour, i.e., compute a shortest "visibility coverage tour". The WRP models a natural problem in robotics, in which a mobile robot/camera is to do a visual inspection of a domain or a part, whose geometry is given. Here, we focus on the offline setting, in which the geometry of the domain P is given; the problem has been studied extensively, both in the offline and online setting (see the surveys [24,25]).In this paper we give the first polynomial-time approximation algorithm for the WRP in polygonal domains in the plane. Our approximation factor is O(log 2 n); we also give the first hardness of approximation result for the WRP, showing that the problem cannot be approximated in polynomial time to within a factor of c log n, for a constant c > 0, assuming that P =NP. Here, n is the number of vertices of P .

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“…However, details are beyond the scope of this thesis. The forthcoming paper [45] is going to continue the investigation with more details.…”

Section: Blocking In An N × N Gridmentioning

confidence: 96%

“…This probability should relate to the threshold has been seen in Section 6.5. To investigate this threshold phenomenon, it is started with the special case of a 2 × N grid, and then proceed to the more general case of an N × N grid [45].…”

Section: The Obstacle Concentration Thresholdmentioning

confidence: 99%

Foraging in the Presence of Obstacles

Wang¹

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This thesis focuses on investigating searching algorithms which can solve the Ants Nearby Treasure Search (ANTS) Problem in the presence of obstacles. In the ANTS problem, there are k ants (modelled as mobile agents) initially located at the origin in a two-dimensional grid. Pheromones are used as physical markers to allow the ants to perform collaborative search. The target treasure is located at an unknown location at distance D from the origin.This thesis studied ant foraging in the systems with and without obstacles. A simple deterministic foraging algorithm is provided first, which uses synchronous identical ants for the environment without obstacle. This simple foraging algorithm is a spiral searching algorithm with comparable complexity to the main algorithm of C. Lenzen and T. Radeva [1]. One significant improvement is that the ants do not need to know the direction in which the nest lies. An extension of this algorithm using an additional marker can achieve a global termination and can allow all the ants to find the target.Further, two additional types of algorithms for ant foraging in a N × N square terrain are introduced. The two types algorithms target different models which contain obstacles in different categories. The Zig-Zag foraging algorithm and the Up-Down foraging algorithm solve the searching problem using a single ant in a bounded environment with large obstacles. It is shown that the ant is able to successfully explore the entire terrain with pheromones provided that the passages between obstacles have width at least five cells. For the second type, the spiral searching algorithms work in the model with k ants in a wrap-around environment having randomly placed single cell obstacles. All of our algorithms are implemented in Netlogo and the corresponding simulations and detail explanations are presented by using examples.

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Optimal Exploration of Terrains with Obstacles

Cited by 5 publications

References 19 publications

Fast collaborative graph exploration

Fast collaborative graph exploration

Approximating Watchman Routes

Foraging in the Presence of Obstacles

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