We present the results of an extensive computational study on dynamic algorithms for all pairs shortest path problems. We describe our implementations of the recent dynamic algorithms of King and of Demetrescu and Italiano, and compare them to the dynamic algorithm of Ramalingam and Reps and to static algorithms on random, real-world and hard instances. Our experimental data suggest that some of the dynamic algorithms and their algorithmic techniques can be really of practical value in many situations. 1

Heuristic search methods promise to find shortest paths for path-planning problems faster than uninformed search methods. Incremental search methods, on the other hand, promise to find shortest paths for series of similar path-planning problems faster than is possible by solving each path-planning problem from scratch. In this article, we develop Lifelong Planning A * (LPA*), an incremental version of A * that combines ideas from the artificial intelligence and the algorithms literature. It repeatedly finds shortest paths from a given start vertex to a given goal vertex while the edge costs of a graph change or vertices are added or deleted. Its first search is the same as that of a version of A * that breaks ties in favor of vertices with smaller g-values but many of the subsequent searches are potentially faster because it reuses those parts of the previous search tree that are identical to the new one. We present analytical results that demonstrate its similarity to A * and experimental results that demonstrate its potential advantage in two different domains if the path-planning problems change only slightly and the changes are close to the goal.

this paper, we extend the GA by adding to it a local improvement procedure, resulting in a memetic algorithm (MA). We compare the MA with an optimized version of the GA and show that the MA not only finds better solutions, but also converges to a given solution in less time

A key functionality in today's widely used interior gateway routing protocols such as OSPF and IS-IS involves the computation of a shortest path tree (SPT). In many existing commercial routers, the computation of an SPT is done from scratch following changes in the link states of the network. As there may coexist multiple SPTs in a network with a set of given link states, such recomputation of an entire SPT not only is inefficient but also causes frequent unnecessary changes in the topology of an existing SPT and creates routing instability. This paper presents a new dynamic SPT algorithm that makes use of the structure of the previously computed SPT. Our algorithm is derived by recasting the SPT problem into an optimization problem in a dual linear programming framework, which can also be interpreted using a ball-andstring model. In this model, the increase (or decrease) of an edge weight in the tree corresponds to the lengthening (or shortening) of a string. By stretching the strings...

) Abstract We consider the problem of maintaining the distances and the shortest paths from a single source in either a directed or an undirected graph with positive real edge weights, handling insertions, deletions and cost updates of edges. We propose fully dynamic algorithms with optimal space requirements and query time. The cost of update operations depends on the class of the considered graph and on the number of vertices that, due to an edge modification, either change their distance from the source or change their parent in the shortest path tree. In the case of graphs with bounded genus (including planar graphs), bounded degree graphs, bounded treewidth graphs and fi-near-planar graphs with bounded fi, the update procedures require O(log n) amortized time per vertex update, while for general graphs with n vertices and m edges they require O( p m log n) amortized time per vertex update. The solution is based on a dynamization of Dijkstra's algorithm [6] and requires simple ...

Heuristic search-based planners, such as HSP 2.0, solve STRIPS-style planning problems efficiently but spend about eighty percent of their planning time on calculating the heuristic values. In this paper, we systematically evaluate alternative methods for calculating the heuristic values for HSP 2.0 and demonstrate that the resulting planning times differ substantially. HSP 2.0 calculates each heuristic value by solving a relaxed planning problem with a dynamic programming method similar to value iteration. We identify two different approaches for speeding up the calculation of heuristic values, namely to order the value updates and to reuse information from the calculation of previous heuristic values. We then show how these two approaches can be combined, resulting in our PINCH method. PINCH outperforms both of the other approaches individually as well as the methods used by HSP 1.0 and HSP 2.0 for most of the large planning problems tested. In fact, it speeds up the planning time of HSP 2.0 by up to eighty percent in several domains and, in general, the amount of savings grows with the size of the domains, allowing HSP 2.0 to solve larger planning problems than was possible before in the same amount of time and without changing its overall operation.

A directed hypergraph is defined by a set of nodes and a set of hyperarcs, each connecting a set of source nodes to a single target node. Directed hypergraphs are used in several contexts to model different combinatorial structures, such as functional dependencies [Ull82], Horn clauses in propositional calculus [AI91], AND-OR graphs [Nil82], Petri nets [Pet62]. A hyperpath, similarly to the notion of path in directed graphs, consists of a connection among nodes using hyperarcs. Unlike paths in graphs, hyperpaths are suitable of different definitions of measure, corresponding to different concepts arising in various applications. In this paper we consider the problem of finding minimal hyperpaths according to several measures. We show that some of these problems are, not surprisingly, NP-hard. However, if the measure function on hyperpaths matches certain conditions (which we define as value-based measure functions) , the problem turns out to be solvable in polynomial time. We...

Given an alphabet Sigma, a (directed) graph G whose edges are weighted and Sigma-labeled, and a formal language L , the Formal Language Constrained Shortest/Simple Path problem consists of finding a shortest (simple) path p in G complying with the additional constraint that l(p) 2 L. Here l(p) denotes the unique word given by concatenating the Sigma-labels of the edges along the path p. The main contributions of this paper include the following: 1. We show that the formal language constrained shortest path problem is solvable efficiently in polynomial time when L is restricted to be a context free language. When L is specified as a regular language we provide algorithms with improved space and time bounds...

Many real-world planning problems require one to solve a series of similar planning tasks. In this case, replanning can be much faster than planning from scratch. In this paper, we introduce a novel replanning method for symbolic planning with heuristic search-based planners, currently the most popular planners. Our SHERPA replanner is not only the first heuristic search-based replanner but, different from previous replanners for other planning paradigms, it also guarantees that the quality of its plans is as good as that achieved by planning from scratch. We provide an experimental feasibility study that demonstrates the promise of SHERPA for heuristic search-based replanning.

In this paper we propose the first experimental study of the fully dynamic single source shortest paths problem on directed graphs with positive real edge weights. In particular, we perform an experimental analysis of three different algorithms: Dijkstra's algorithm, and the two output bounded algorithms proposed by Ramalingam and Reps in [31] and by Frigioni, Marchetti-Spaccamela and Nanni in [18], respectively. The main goal of this paper is to provide a first experimental evidence for: (a) the effectiveness of dynamic algorithms for shortest paths with respect to a traditional static approach to this problem; (b) the validity of the theoretical model of output boundedness to analyze dynamic graph algorithms. Beside random generated graphs, useful to capture the "asymptotic" behavior of algorithms, we also develope experiments by considering a widely used graph from the real world, i.e., the Internet graph. Work partially supported by the ESPRIT Long Term Research Project...