Localization on Discrete Grid Graphs

Gorbenko, Anna; Popov, Vladimir; Sheka, Andrey

doi:10.1007/978-94-007-1839-5_105

Cited by 34 publications

(17 citation statements)

References 7 publications

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“…Now, using standard transformations (see e.g. [ [18] for natural instances, N3 is the reduction from [19] for natural instances, R1 is ζ for robotic instances, R2 is γ [1] from [18] for robotic instances, R3 is the reduction from [19] for robotic instances.…”

Section: G(a[n] B[n]) Is a Hamilton Path In G Now Let G(a[1]mentioning

confidence: 99%

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On Hamilton paths in grid graphs

Gorbenko¹,

Popov²

2013

astp

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In this paper we consider an approach to solve the Hamilton path problem for grid graphs. This approach is based on an explicit reduction from the problem to the satisfiability problem. Gridworlds are extensively used for design of experiments as models of real world. In particular, grid graphs are popular testbeds for different hard problems. In particular, grid graphs used for investigation of robotic planning problems (see e.g. [1]). For instance, grid graph can be considered as a map of some indoor environment. Vacuum cleaning robot needs cover the environment. The robot must visit each vertex only once to prevent a damage of the floor. It is clear that we can consider the Hamilton path problem (HP) for grid graphs as a model for this robotic problem. In this paper we consider an approach to solve HP. Note that HP is NP-complete [2]. Encoding different hard problems as instances of SAT has caused considerable interest (see e.g. PACS[3] - [15]). We consider an explicit reduction from HP to the satisfiability problem.

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Section: G(a[n] B[n]) Is a Hamilton Path In G Now Let G(a[1]mentioning

confidence: 99%

“…, G(i n , j n )}, (G(i, j), G(s, t)) ∈ E ⇔ |i − s| + |j − t| = 1 ∧ {G(i, j), G(s, t)} ⊆ V . Also, we can assume that 1 …”

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confidence: 99%

On Hamilton paths in grid graphs

Gorbenko¹,

Popov²

2013

astp

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“…However, for practical application of difficult instances we need a method for their fast decision. Some practical applications of VDLPP were considered in [2]. Also, the authors of [2] were proposed to use an explicit polynomial reduction from VDLPP to satisfiability problems to obtain solutions for difficult instances of VDLPP.…”

Section: Introductionmentioning

confidence: 99%

On the valid deterministic localization plan problem

Sheka¹

2013

ams

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Grid graphs are popular testbeds for planning with incomplete information. In particular, it is studied a fundamental planning problem, localization, to investigate whether gridworlds make good testbeds for planning with incomplete information. It is found empirically that greedy planning methods that interleave planning and plan execution can localize robots very quickly on random gridworlds or mazes. Thus, they may not provide adequately challenging testbeds. On the other hand, it is showed that finding localization plans that are within a log factor of optimal is NP-hard. Thus there are instances of gridworlds on which all greedy planning methods perform very poorly. These theoretical results help empirical researchers to select appropriate planning methods for planning with incomplete information as well as testbeds to demonstrate them. However, for practical application of difficult instances we need a method for their fast decision. In this paper, we consider an approach to solve localization problem. In particular, we consider an explicit polynomial reduction from the decision version of the valid deterministic localization plan problem to the 3-satisfiability problem. Mathematics Subject Classification: 68T40

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“…In particular, we can mention problems of robot visual navigation (see e.g. [4] - [11]). In this paper, we consider the problem of monitoring of passenger flows.…”

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confidence: 99%