Faster Algorithms For The Shortest Path Problem

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Excerpt from Faster Algorithms for the Shortest Path Problem Surprisingly, these two directions have not been very complementary. The algorithms that achieve the best worst-case complexity have generally not been attractive empirically and the algorithms that have performed well in practice have generally failed to have an attractive worst-case bound. In this paper, we present new implementations of Dijkstra's algorithm intended to bridge this gap. Under the assumption that arc lengths are bounded by a polynomial function of n these algorithms achieve the best possible worst-case complexity for all but very sparse graphs and yet are simple enough to be efficient in practice. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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This book constitutes the refereed proceedings of the 33rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2007, held in Harrachov, Czech Republic in January 2007. The 69 revised full papers, presented together with 11 invited contributions were carefully reviewed and selected from 283 submissions. The papers were organized in four topical tracks.

Excerpt from Faster Parametric Shortest Path and Minimum Balance Algorithms The second section describes the minimum mean cycle problem and how the parametric shortest path algorithm can be used to solve it. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

An extensively revised edition of a mathematically rigorous yet accessible introduction to algorithms.

Real-life decision-making problem has been demonstrated to cover the indeterminacy through single valued neutrosophic set. It is the extension of interval valued neutrosophic set. Most of the problems of real life involve some sort of uncertainty in it among which, one of the famous problem is finding a shortest path of the network. In this paper, a new score function is proposed for interval valued neutrosophic numbers and SPP is solved using interval valued neutrosophic numbers. Additionally, novel algorithms are proposed to find the neutrosophic shortest path by considering interval valued neutrosophic number, trapezoidal and triangular interval valued neutrosophic numbers for the length of the path in a network with illustrative example. Further, comparative analysis has been done for the proposed algorithm with the existing method with the shortcoming and advantage of the proposed method and it shows the effectiveness of the proposed algorithm.