A generalization of Dijkstra's shortest path algorithm with applications to VLSI routing

Peyer, Sven; Rautenbach, Dieter; Vygen, Jens

doi:10.1016/j.jda.2007.08.003

Cited by 77 publications

(42 citation statements)

References 36 publications

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“…This could also provide an even wider coverage of potential gene-protein functional interaction space. Furthermore, search methods such as shortest path (Peyer et al, 2009) or PageRank (Brin and Page, 1998) could be implemented to exploit other topological properties of the network and to test the suitability of different types of search methods and queries. Fig.…”

Section: Discussionmentioning

confidence: 99%

MaxLink: network-based prioritization of genes tightly linked to a disease seed set

2014

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Summary: MaxLink, a guilt-by-association network search algorithm, has been made available as a web resource and a stand-alone version. Based on a user-supplied list of query genes, MaxLink identifies and ranks genes that are tightly linked to the query list. This functionality can be used to predict potential disease genes from an initial set of genes with known association to a disease. The original algorithm, used to identify and rank novel genes potentially involved in cancer, has been updated to use a more statistically sound method for selection of candidate genes and made applicable to other areas than cancer. The algorithm has also been made faster by re-implementation in C++, and the Web site uses FunCoup 3.0 as the underlying network. Availability and implementation: MaxLink is freely available at http:// maxlink.sbc.su.se both as a web service and a stand-alone application for download.

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Section: Discussionmentioning

confidence: 99%

MaxLink: network-based prioritization of genes tightly linked to a disease seed set

2014

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“…Eklund [32] presented the modi ed Dijkstra's algorithm that includes both static and dynamic components, simultaneously used for routing the emergency vehicles in the simulation of earthquake in Okayama, Japan. In the paper by Peyer [33], a new algorithm called Generalized Dijkstra was introduced which is a fast technique for Dijkstra's algorithm. Its di erence from the previous method is labeling on the set of vertices, instead of labeling on each vertex.…”

Section: Literature Of Dijkstra's Algorithmmentioning

confidence: 99%

The combination of TOPSIS method and Dijkstra’s algorithm in multi-attribute routing

Roghanian

Kebria

2017

Scientia Iranica

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Abstract. This paper introduces a new method called multi-attribute Dijkstra that is an extension of Dijkstra used to determine the shortest path between two points of a graph while arcs between the points, in addition to the distance, have other attributes such as time (distance), cost, emissions, risk, etc. Technique for order preferences by similarity to the ideal (TOPSIS) method is used for ranking and selecting the routes which is a method for solving Multi-Attribute Decision-Making problems (MADM). In this regard, we try to choose appropriate weights for the attributes to consider the right decision for creating a balance between the e ective elements in route selection. In this paper, the algorithm of Dijkstra and TOPSIS will be reviewed, and the proposed method obtained by the combination of these two will also be described. Finally, three examples with di erent conditions are presented to represent the performance of the model. Then, these examples are compared with single-attribute Dijkstra to realize the e ectiveness of the proposed method. Obviously, in solving large-scale examples, the approach is based on coding in appropriate software.

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“…The goal is to solve large-scale size problems in reasonable time. In order to deal with large networks, some papers (Peyer et al 2009;Jigang et al 2010;Sven Peyera and Rautenbachb 2009) introduced a divide-and-conquer strategy to partition the graph into small subgraphs and materialize the shortestpaths between border nodes in different subgraphs. In Peyer et al (2009), the authors proposed a generalization of Dijkstra's shortest path algorithm to deal with applications of VLSI routing.…”

Section: Related Workmentioning

confidence: 99%

“…A*, with a consistent heuristic, is usually faster than Dijkstra, in practice, for finding the shortest path between two nodes, but Dijkstra algorithm has the advantage of calculating all distances from one node to all other nodes on the graph, in a single run. Nevertheless, these two algorithms may be inefficient in terms of computation time for large-scale grid environments (Potamias et al 2009;Jigang et al 2010;Kanoulas et al 2006;Sven Peyera and Rautenbachb 2009), since the Dijkstra's algorithm has a quadratic time complexity O(n 2 ) and processes the whole grid to find the optimal path and A* algorithm may be time consuming to reach the optimal solution for hard instances (such as mazes) depending on the density of obstacles. In order to overcome these drawbacks, we propose two novel and efficient approaches called Relaxed Dijkstra (RD) and Relaxed A* (RA*) to improve the basic Dijkstra and A* algorithms, in the specific case of regular grid environments.…”

Section: Introductionmentioning

confidence: 99%

Relaxed Dijkstra and A* with linear complexity for robot path planning problems in large-scale grid environments

et al. 2015

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Although there exist efficient methods to determine an optimal path in a graph, such as Dijkstra and A* algorithms, large instances of the path planning problem need more adequate and efficient techniques to obtain solutions in reasonable time. We propose two new time-linear relaxed versions of Dijkstra (RD) and A* (RA*) algorithms to solve the global path planning problem in large grid environments. The core idea consists in exploiting the grid-map structure to establish an accurate approximation of the optimal path, Communicated by V. Loia. B Imen Châari without visiting any cell more than once. We conducted extensive simulations (1290 runs on 43 maps of various types) for the proposed algorithms, both in four-neighbor and eight-neighbor grid environments, and compared them against original Dijkstra and A* algorithms with different heuristics. We demonstrate that our relaxed versions exhibit a substantial gain in terms of computational time (more than 3 times faster in average), and in most of tested problems an optimal solution (in at least 97 % of cases for RD and 82 % for RA*) or a very close one is reached (at most 9 % of extra length, and less than 2 % in average). Besides, the simulations also show that RA* provides a better trade-off between solution quality and execution time than previous bounded relaxations of A* that exist in the literature.

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A generalization of Dijkstra's shortest path algorithm with applications to VLSI routing

Cited by 77 publications

References 36 publications

MaxLink: network-based prioritization of genes tightly linked to a disease seed set

MaxLink: network-based prioritization of genes tightly linked to a disease seed set

The combination of TOPSIS method and Dijkstra’s algorithm in multi-attribute routing

Relaxed Dijkstra and A* with linear complexity for robot path planning problems in large-scale grid environments

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