Level graphs and approximate shortest path algorithms

Shapiro, Jacob; Waxman, Jerry; Nir, Danny

doi:10.1002/net.3230220707

Cited by 30 publications

(21 citation statements)

References 4 publications

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“…fewer intersections). A modification of the weighting function could easily be used to explicitly prefer certain types of road [10,11,12]. For example, major roads could be preferred in the route selection by making the weights for turning onto a major road smaller, and turning off a major road larger.…”

Section: Discussionmentioning

confidence: 99%

“…Shortest path algorithms only minimize route efficiency, in terms of distance or travel cost, and not route description complexity. Algorithms for finding an optimal route that is not the shortest path have been proposed by Shapiro et al [10] as well as Liu [11,12]. The approach of Shapiro et al can be used to take advantage of the type of roads (major roads versus minor roads), generating a route that prefers major routes.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

“Simplest” Paths: Automated Route Selection for Navigation

Duckham

Kulik

2003

Spatial Information Theory. Foundations of Geographic Information Science

159

155

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Abstract. Numerous cognitive studies have indicated that the form and complexity of route instructions may be as important to human navigators as the overall length of route. Most automated navigation systems rely on computing the solution to the shortest path problem, and not the problem of finding the "simplest" path. This paper addresses the issue of finding the "simplest" paths through a network, in terms of the instruction complexity. We propose a "simplest" paths algorithm that has quadratic computation time for a planar graph. An empirical study of the algorithm's performance, based on an established cognitive model of navigation instruction complexity, revealed that the length of a simplest path was on average only 16% longer than the length of the corresponding shortest path. In return for marginally longer routes, the simplest path algorithm seems to offer considerable advantages over shortest paths in terms of their ease of description and execution. The conclusions indicate several areas for future research: in particular cognitive studies are needed to verify these initial computational results. Potentially, the simplest paths algorithm could be used to replace shortest paths algorithms in any automated system for generating human navigation instructions, including in-car navigation systems, Internet driving direction servers, and other location-based services.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“Simplest” Paths: Automated Route Selection for Navigation

Duckham

Kulik

2003

Spatial Information Theory. Foundations of Geographic Information Science

159

155

View full text Add to dashboard Cite

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“…Although many path optimizations focused on distance travelled minimum are not aiming at reducing path simplicity, this reduction is their byproduct. A path solution could prefer major road by incorporating road network knowledge, which has lower simplicity before optimizing (8,9). Based on the topology representation of graph, an algorithm was presented to compute all fewest-turn paths using natural roads connectivity (10).…”

Section: Introductionmentioning

confidence: 99%

A fewest-turn-and-shortest path algorithm based on breadth-first search

Zhou

Wang

et al. 2014

Geo-spatial Information Science

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Many cognitive studies have indicated that the path simplicity may be as important as its distance travelled. However, the optimality of paths for current navigation system is often judged purely on the distance travelled or time cost, and not the path simplicity. To balance these factors, this paper presented an algorithm to compute a path that not only possesses fewest turns but also is as short as possible by utilizing the breadth-first-search strategy. The proposed algorithm started searching from a starting point, and expanded layer by layer through searching zero-level reachable points until the endpoint is found, and then deleted unnecessary points in the reverse direction. The forward searching and backward cleaning strategies were presented to build a hierarchical graph of zero-level reachable points, and form a fewestturn-path graph (G*). After that, a classic Dijkstra shortest path algorithm was executed on the G* to obtain a fewestturn-and-shortest path. Comparing with the shortest path in Baidu map, the algorithm in this work has less than half of the turns but the nearly same length. The proposed fewest-turn-and-shortest path algorithm is proved to be more suitable for human beings according to human cognition research.

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“…By solving for all pairs of shortest paths in the higher level subnetwork and interfacing with gateways into the lower level subnetworks, we achieve significant economics of computation, albeit at the expense of a loss of optimality. We explore in this article the magnitudes of the computational gains and associated errors from optimality.A similar approach is taken by Shapiro, Waxman, and Nir, [8] who classify each of the arcs in the network, and approximate shortest paths based on the assumption that it is desirable to spend as little time as possible on lower level arcs. Their approach can be very efficient, especially when only a few shortest paths need to be computed.…”

mentioning

confidence: 99%

“…A similar approach is taken by Shapiro, Waxman, and Nir, [8] who classify each of the arcs in the network, and approximate shortest paths based on the assumption that it is desirable to spend as little time as possible on lower level arcs. Their approach can be very efficient, especially when only a few shortest paths need to be computed.…”

mentioning

confidence: 99%

Approximating Shortest Paths in Large-Scale Networks with an Application to Intelligent Transportation Systems

Chou¹,

Romeijn

Smith

1998

INFORMS Journal on Computing

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We propose a hierarchical algorithm for approximating shortest paths between all pairs of nodes in a large-scale network. The algorithm begins by extracting a high-level subnetwork of relatively long links (and their associated nodes) where routing decisions are most crucial. This high-level network partitions the shorter links and their nodes into a set of lower-level subnetworks. By fixing gateways within the high-level network for entering and exiting these subnetworks, a computational savings is achieved at the expense of optimality. We explore the magnitude of these tradeoffs between computational savings and associated errors both analytically and empirically with a case study of the Southeast Michigan traffic network. An orderof-magnitude drop in computation times was achieved with an on-line route guidance simulation, at the expense of less than 6% increase in expected trip times.O ur interest in this article is directed toward solving very large-scale shortest path problems, motivated by the problem of finding minimum travel time paths within an on-line route guidance system. Route guidance within the context of Intelligent Transportation Systems is the task of providing routes between origins and destinations that promise to minimize the trip times experienced. The link travel times that are provided as an input to this function are timedependent forecasts based upon current and anticipated traffic congestion (see e.g., Kaufman and Smith, [7] Wunderlich and Smith [9] ). Because of the rapid change of link travel times caused by time-varying travel demands and lane blockage resulting from incidents, the data used in computing the shortest paths information is updated periodically, ideally every 5 to 10 minutes. During the time interval between data updates, a shortest path must be provided for every origin/destination (O/D) associated with trips that begin during that time slice. Thus, the calculation of shortest paths must be efficient enough to respond in a timely way to trip requests on a real-time basis. Because a realistic problem may have hundreds of thousands of nodes, all of which may be potential origins and destinations, a fast heuristic that can provide good approximations in a limited amount of time may be preferred to exact methods.We present here a hierarchical approach for finding approximate solutions for shortest path problems. A key idea behind our development is the imposition of a hierarchical network structure. Our approach is motivated by the observation that traffic networks have a hierarchical structure that divides links (and nodes corresponding to intersections of these links) into two or more classes (Yagyu et al. [10] ). The higher level corresponds to longer links (i.e., highways) where the frequency of decision opportunities is low, with routing decisions being correspondingly more important. The lower level corresponds to links of limited duration (i.e., surface streets) and, correspondingly, more opportunities to correct routing decision errors. The links and nodes compri...

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Level graphs and approximate shortest path algorithms

Cited by 30 publications

References 4 publications

“Simplest” Paths: Automated Route Selection for Navigation

“Simplest” Paths: Automated Route Selection for Navigation

A fewest-turn-and-shortest path algorithm based on breadth-first search

Approximating Shortest Paths in Large-Scale Networks with an Application to Intelligent Transportation Systems

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