This paper is a state of the art on the shortest path problems for which it exists uncertainty and inaccuracy factors on arc values. Two uncertainty models are distinguished: the so-called interval model and the discrete set of scenarios model. Different measures and approaches of robustness are presented: those coming from decision theory, those coming from multicriteria analysis and those com...

In this paper, we consider Dijkstra’s algorithm for the single source single target shortest path problem in large sparse graphs. The goal is to reduce the response time for on-line queries by using precomputed information. Due to the size of the graph, preprocessing space requirements can be only linear in the number of nodes. We assume that a layout of the graph is given. In the preprocessing...

This document describes the QSPN, the routing discovery algorithm used by Netsukuku. Through a deductive analysis the main proprieties of the QSPN are shown. Moreover, a second version of the algorithm, is presented. i ar X iv :0 70 5. 08 17 v1 [ cs .N I] 6 M ay 2 00 7 This document is part of Netsukuku. Copyright c ©2007 Andrea Lo Pumo aka AlpT . All rights reserved. This do...

In this paper, we report on our own experience in studying a fundamental problem on graphs: all pairs shortest paths. In particular, we discuss the interplay between theory and practice in engineering a simple variant of Dijkstra’s shortest path algorithm. In this context, we show that studying heuristics that are efficient in practice can yield interesting clues to the combinatorial properties...

Exact implementations of algorithms of computational geometry are subject to exponential growth in running time and space. This exponential growth arises when the algorithms are cascaded: the output of one algorithm becomes the input to the next. Cascading is a signiicant problem in practice. We propose a geometric rounding technique: shortest path rounding. Shortest path rounding trades accura...

This paper proposes and solves a-autonomy and k-stops shortest path problems in large spatial databases. Given a source s and a destination d, an aautonomy query retrieves a sequence of data points connecting s and d, such that the distance between any two consecutive points in the path is not greater than a. A k-stops query retrieves a sequence that contains exactly k intermediate data points....

We consider the problem of classifying graphs using graph kernels. We define a new graph kernel, called the generalized shortest path kernel, based on the number and length of shortest paths between nodes. For our example classification problem, we consider the task of classifying random graphs from two well-known families, by the number of clusters they contain. We verify empirically that the ...

Shortest path is a fundamental graph problem with numerous applications. However, the concept of classic shortest path is insufficient or even flawed in a temporal graph, as the temporal information determines the order of activities along any path. In this paper, we show the shortcomings of classic shortest path in a temporal graph, and study various concepts of “shortest” path for temporal gr...

We consider dynamic, two-player, zero-sum games where the \minimizing" player seeks to drive an underlying nite-state dynamic system to a special terminal state along a least expected cost path. The \maximizer" seeks to interfere with the minimizer's progress so as to maximize the expected total cost. We consider, for the rst time, undiscounted nite-state problems, with compact action spaces, a...

We propose shortest path algorithms that use A* semch in combination with a new graph-theoretic lower-bounding technique based on landmarks and the triangle inequality. Our algorithms compute optimal shortest paths and work on any directed graph. We give experimental results showing that the most efficient of our new algorithms outperforms previous algorithms, in particular A* search with Eucli...