Search results for "Shortest Path Faster Algorithm"
showing 4 items of 4 documents
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…