Search results for "K short"
showing 9 items of 9 documents
Asymmetry matters: Dynamic half-way points in bidirectional labeling for solving shortest path problems with resource constraints faster
2017
Abstract With their paper “Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints” [Discrete Optimization 3, 2006, pp. 255–273] Righini and Salani introduced bounded bidirectional dynamic programming (DP) as an acceleration technique for solving variants of the shortest path problem with resource constraints (SPPRC). SPPRCs must be solved iteratively when vehicle routing and scheduling problems are tackled via Lagrangian relaxation or column-generation techniques. Righini and Salani and several subsequent works have shown that bounded bidirectional DP algorithms are often superior to their monodirectional counterparts, s…
Implementation of algorithms forK shortest loopless paths
1986
Implementations of loopless k shortest path algorithms are examined. Efficient storage structures for a large number of paths are given. A fast algorithm for determining the shortest paths in Yen's method is developed. Timing experiments show that a hybrid of Clarke's and Yen's methods is generally the fastest, although not significantly. Using upper bounds for the lengths of paths essentially improves all methods.
The computational complexity of the relative robust shortest path problem with interval data
2004
Abstract The paper deals with the relative robust shortest path problem in a directed arc weighted graph, where arc lengths are specified as intervals containing possible realizations of arc lengths. The complexity status of this problem has been unknown in the literature. We show that the problem is NP -hard.
A class of label-correcting methods for the K shortest paths problem
2001
In this paper we deal with the problem of finding the first K shortest paths from a single origin node to all other nodes of a directed graph. In particular, we define the necessary and sufficient conditions for a set of distance label vectors, on the basis of which we propose a class of methods which can be viewed as an extension of the generic label-correcting method for solving the classical single-origin all-destinations shortest path problem. The data structure used is characterized by a set of K lists of candidate nodes, and the proposed methods differ in the strategy used to select the node to be extracted at each iteration. The computational results show that: 1. some label-correct…
The Spanning Tree based Approach for Solving the Shortest Path Problem in Social Graphs
2016
Nowadays there are many social media sites with a very large number of users. Users of social media sites and relationships between them can be modelled as a graph. Such graphs can be analysed using methods from social network analysis (SNA). Many measures used in SNA rely on computation of shortest paths between nodes of a graph. There are many shortest path algorithms, but the majority of them suits only for small graphs, or work only with road network graphs that are fundamentally different from social graphs. This paper describes an efficient shortest path searching algorithm suitable for large social graphs. The described algorithm extends the Atlas algorithm. The proposed algorithm so…
On the Greedy Algorithm for the Shortest Common Superstring Problem with Reversals
2015
We study a variation of the classical Shortest Common Superstring (SCS) problem in which a shortest superstring of a finite set of strings $S$ is sought containing as a factor every string of $S$ or its reversal. We call this problem Shortest Common Superstring with Reversals (SCS-R). This problem has been introduced by Jiang et al., who designed a greedy-like algorithm with length approximation ratio $4$. In this paper, we show that a natural adaptation of the classical greedy algorithm for SCS has (optimal) compression ratio $\frac12$, i.e., the sum of the overlaps in the output string is at least half the sum of the overlaps in an optimal solution. We also provide a linear-time implement…
Optimal Paths on Urban Networks Using Travelling Times Prevision
2012
We deal with an algorithm that, once origin and destination are fixed, individuates the route that permits to reach the destination in the shortest time, respecting an assigned maximal travel time, and with risks measure below a given threshold. A fluid dynamic model for road networks, according to initial car densities on roads and traffic coefficients at junctions, forecasts the future traffic evolution, giving dynamical weights to a constrained 𝐾 shortest path algorithm. Simulations are performed on a case study to test the efficiency of the proposed procedure.
A parallel simulated annealing approach to the K shortest loopless paths problem
1997
The k shortest loopless paths problem is a significant combinatorial problem which arises in many contexts. When the size of the networks is very large the exact algorithms fail to find the best solution in a reasonable time. The aim of this paper is to suggest parallel efficient algorithms to obtain a good approximation of the solution to the k shortest loopless paths problem between two arbitrary nodes, when the network size is large. The heuristic used is known in literature as Simulated Annealing. Preliminary tests have been conducted for evaluating the validity of the proposed algorithms. The quality of the obtained results represents a significant base for further experimentations.
A measurement of the K-S lifetime
2002
A measurement of the K_S lifetime is presented using data recorded by the NA48 experiment at the CERN-SPS during 1998 and 1999. The K_S lifetime is derived from the ratio of decay time distributions in simultaneous, collinear K_S and K_L beams, giving a result which is approximately independent of the detector acceptance and with reduced systematic errors. The result obtained is tau_S=(0.89598 +- 0.00048 +- 0.00051)x10^(-10) s, where the first error is statistical and the second systematic.