A linear-time algorithm for the longest path problem in rectangular grid graphs

Keshavarz-Kohjerdi, Fatemeh; Bagheri, Alireza; Asgharian-Sardroud, Asghar

doi:10.1016/j.dam.2011.08.010

Cited by 28 publications

(16 citation statements)

References 8 publications

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“…For works on the longest paths in undirected graphs (random), refer to [25][26][27]. Algorithms for approximating the longest paths in grid graphs and meshes can be seen here [28][29][30][31][32]. There are methods that are based on the longest paths in random graphs (for example, see [25]) and search for the trees formed by probability processes [33,34].…”

Section: Related Workmentioning

confidence: 99%

Understanding chicken walks on n × n grid: Hamiltonian paths, discrete dynamics, and rectifiable paths

Rao

Tomley

Blake

2014

Math Methods in App Sciences

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Communicated by R. Bravo de la ParraUnderstanding animal movements and modeling the routes they travel can be essential in studies of pathogen transmission dynamics. Pathogen biology is also of crucial importance, defining the manner in which infectious agents are transmitted. In this article, we investigate animal movement with relevance to pathogen transmission by physical rather than airborne contact, using the domestic chicken and its protozoan parasite Eimeria as an example. We have obtained a configuration for the maximum possible distance that a chicken can walk through straight and nonoverlapping paths (defined in this paper) on square grid graphs. We have obtained preliminary results for such walks which can be practically adopted and tested as a foundation to improve understanding of nonairborne pathogen transmission. Linking individual nonoverlapping walks within a grid-delineated area can be used to support modeling of the frequently repetitive, overlapping walks characteristic of the domestic chicken, providing a framework to model fecal deposition and subsequent parasite dissemination by fecal/host contact. We also pose an open problem on multiple walks on finite grid graphs. These results grew from biological insights and have potential applications.

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Section: Related Workmentioning

confidence: 99%

Understanding chicken walks on n × n grid: Hamiltonian paths, discrete dynamics, and rectifiable paths

Rao

Tomley

Blake

2014

Math Methods in App Sciences

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“…In this paper, we present a sequential and a parallel algorithms for finding longest paths between two given vertices in rectangular grid graphs (meshes). Our algorithm has improved the previous algorithm [13] by reducing the number of partition steps from O(m + n) to only a constant.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, Zhang and Liu [25] gave an approximation algorithm for the longest path problem in grid graphs and their algorithm runs in quadratic time. Also the authors in [13] has been studied the longest path problem for rectangular grid graphs and their algorithm is based on divide and conquer technique and runs in linear time. Some results of the grid graphs are investigated in [14,20].…”

Section: Introductionmentioning

confidence: 99%

An efficient parallel algorithm for the longest path problem in meshes

Keshavarz-Kohjerdi

Bagheri

2013

J Supercomput

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“…Recently, Keshavarz-Kohjerdi and Bagheri [22] gave the necessary and sufficient conditions for the existence of Hamiltonian paths in alphabet grid graphs, and presented linear-time algorithms for finding Hamiltonian paths with two given endpoints in these graphs. Recently, Keshavarz-Kohjerdi et al [23] presented a linear-time algorithm for computing the longest path between any two given vertices in rectangular grid graphs. Reay and Zamfirescu [31] proved that all 2-connected, linear-convex triangular grid graphs except one special case contain Hamiltonian cycles.…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian cycles in linear-convex supergrid graphs

Hung

2016

Discrete Applied Mathematics

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A supergrid graph is a finite induced subgraph of the infinite graph associated with the two-dimensional supergrid. The supergrid graphs contain grid graphs and triangular grid graphs as subgraphs. The Hamiltonian cycle problem for grid and triangular grid graphs was known to be NP-complete. In the past, we have shown that the Hamiltonian cycle problem for supergrid graphs is also NP-complete. The Hamiltonian cycle problem on supergrid graphs can be applied to control the stitching trace of computerized sewing machines. In this paper, we will study the Hamiltonian cycle property of linear-convex supergrid graphs which form a subclass of supergrid graphs. A connected graph is called k-connected if there are k vertex-disjoint paths between every pair of vertices, and is called locally connected if the neighbors of each vertex in it form a connected subgraph. In this paper, we first show that any 2-connected, linear-convex supergrid graph is locally connected. We then prove that any 2-connected, linear-convex supergrid graph contains a Hamiltonian cycle.

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A linear-time algorithm for the longest path problem in rectangular grid graphs

Cited by 28 publications

References 8 publications

Understanding chicken walks on n × n grid: Hamiltonian paths, discrete dynamics, and rectifiable paths

Understanding chicken walks on n × n grid: Hamiltonian paths, discrete dynamics, and rectifiable paths

An efficient parallel algorithm for the longest path problem in meshes

Hamiltonian cycles in linear-convex supergrid graphs

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