On the K shortest path trees problem

González-Martín, Carlos

doi:10.1016/j.ejor.2009.06.017

Cited by 16 publications

(6 citation statements)

References 22 publications

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“…Other authors [13], proposed solutions to find the shortest path using Network Simplex Method. And may also find in the literature other methods to solve the routing problems, such: Genetic Algorithms [14], Branch and Bound methods [15]; insertion heuristics [16], Tabu Search [17] and constrained shortest path relaxation [18].…”

Section: Background and Related Workmentioning

confidence: 99%

Time enhanced A*: Towards the development of a new approach for Multi-Robot Coordination

Santos

Costa

Rocha

et al. 2015

2015 IEEE International Conference on Industrial Technology (ICIT)

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In this paper the authors focus on presenting a new path planning approach for a multi-robot transportation system in an industrial case scenario. The proposed method is based on the A* heuristic search in a cell decomposition scenario, for which a time component was added -Time Enhanced A* or simply TEA*.To access the flexibility and efficiency of the proposed algorithm, a set of experiments were performed in a simulated industrial environment. During trials execution the proposed algorithm has shown high capability on preventing/dealing with the occurrence of deadlocks in the transportation system.

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Section: Background and Related Workmentioning

confidence: 99%

Time enhanced A*: Towards the development of a new approach for Multi-Robot Coordination

Santos

Costa

Rocha

et al. 2015

2015 IEEE International Conference on Industrial Technology (ICIT)

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“…In line 15, we need to update the value of arcs which smaller values have been found for them in the recent iteration which will be called DECREASE-KEY. If as Yang and Chen [15] Fibonacci heap [22] is used, the time complexity of each EXTRACT-MIN operation will be O(log m) and the time complexity of each DECREASE-KEY operation will be O (1).…”

Section: Time and Space Complexity Of The Algorithmmentioning

confidence: 99%

“…In this definition, r is the maximum number of green and red light time windows in a single cycle among all traffic light timings which are used in the traffic network. Notice that 1) when total duration of a class is passed (after TLT [i].RLD [r]), the sequence of time windows will be restarted from first time window (TLT [i].GLD [1]), 2) if number of used green and red durations was less than r in a timing, the unused durations will be set to zero.…”

Section: Td == Tlt[i]gld[1] + Tlt[i]rld[1]+ Tlt[i]gld[2] + Tlt[i]mentioning

confidence: 99%

“…2, when the current time of the system is equal to start time of class i of TLTs (SystemTime == TLT [i].ST), the state transition diagram will be started with first green light duration. The timer will be stayed in first green light for TLT [i].GLD [1] seconds and then moves to the first red light duration. Again, it will be stayed in this state for TLT [i].RLD [i] seconds and then moves to the second green light.…”

Section: Timers and State Transition Diagrammentioning

confidence: 99%

“…Basically, the shortest path problem is concerned to find the path with minimum distance, time, or cost from an origin to a destination (or all other nodes) in a connected network e.g. [1]- [4]. Shortest path problem is an important and classic problem in the combinatorial optimization field due to its numerous applications especially in transportation and data communication.…”

Section: Introductionmentioning

confidence: 99%

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Shortest paths in synchronized traffic-light networks

Khanjary

Faez

Meybodi

et al. 2011

2011 24th Canadian Conference on Electrical and Computer Engineering(CCECE)

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The time-constrained shortest path problem is an important generalization of the shortest path problem. The basic feature in time-constrained shortest path problem is considering when a node in the network can be visited under some time constraints. In this paper, a label-setting shortest path algorithm will be proposed to use in the synchronized traffic-light networks which uses the waiting times for green light (node costs) as well as the required times to pass the streets (link costs) to calculate the optimal routes.

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k-Best Enumeration

Eppstein¹

2016

Encyclopedia of Algorithms

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We survey k-best enumeration problems and the algorithms for solving them, including in particular the problems of finding the k shortest paths, k smallest spanning trees, and k best matchings in weighted graphs.in both the input size and k. There are two general techniques that can be used to achieve this, based on optimal substructures and solution space partitioning. In turn, these methods rely on fast algorithms for the selection problem in certain sets of structured values. SelectionUnderlying many k-best algorithms is the problem of selection, finding the k smallest values from a larger set of values [21]. If there are n values in the set, then selection may be solved in time O(n + k), for instance by quickselect, an algorithm that chooses a random pivot value from the set, partitions the rest of the set into subsets that are less than, equal to, or greater than the pivot, and then recurses into one of these subsets [131].However, in k-best problems, we do not wish to generate all solutions before finding the best of them: we wish to avoid the O(n) part of this O(n + k) time bound. Often, the solution values among which we are selecting the k best have some additional structure that allows finding the k best without examining all solutions. For instance, suppose that the space of solutions can be represented as the vertex set of an (implicitly defined) edge-weighted graph, that the degrees of the vertices in this graph are bounded, and that the quality of any particular solution equals the length of the shortest path in this graph from some designated starting vertex to the solution vertex. In such a case, Dijkstra's algorithm can be used to recover the k smallest of these values in time O(k log k), independent of the size of the graph, without requiring that the whole graph be explored. Other structures that allow the k best solutions to be found more efficiently than enumeration of the whole solution set include representations of the solution space as the set of sums of pairs of values drawn from two sorted sets [76,111], or as the elements of an (implicitly defined) matrix whose rows and columns are sorted [77]. Again, for such structures, the k smallest values can be found efficiently without examining the whole matrix or the whole set of pair sums.A general framework that can be used to describe many of these structured selection problems is the problem of selection in a d-ary heap. A min-heap is a rooted tree, with values associated with its nodes, such that each non-root node has a value that is at least as large as its parent. In order to avoid having to construct all solutions before performing a selection algorithm, and in order to handle situations in which this tree has infinitely many nodes, we will assume that our selection algorithm is given as input an implicit representation of such a heap. That is, its input consists of a binary representation of the root node of the heap together with pointers to two subroutines that take a single node as input: one subroutine to list the children of any...

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On the K shortest path trees problem

Cited by 16 publications

References 22 publications

Time enhanced A*: Towards the development of a new approach for Multi-Robot Coordination

Time enhanced A*: Towards the development of a new approach for Multi-Robot Coordination

Shortest paths in synchronized traffic-light networks

k-Best Enumeration

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