Results 11  20
of
43
Maintaining Shortest Paths in Digraphs with Arbitrary Arc Weights: An Experimental Study
 In Proc. Workshop on Algorithm Engineering
, 2000
"... We present the first experimental study of the fully dynamic singlesource shortest paths problem in digraphs with arbitrary (negative and nonnegative) arc weights. We implemented and tested several variants of the theoretically fastest fully dynamic algorithms proposed in the literature, plus ..."
Abstract

Cited by 11 (2 self)
 Add to MetaCart
We present the first experimental study of the fully dynamic singlesource shortest paths problem in digraphs with arbitrary (negative and nonnegative) arc weights. We implemented and tested several variants of the theoretically fastest fully dynamic algorithms proposed in the literature, plus a new algorithm devised to be as simple as possible while matching the best worstcase bounds for the problem. According to experiments performed on randomly generated test sets, all the considered dynamic algorithms are faster by several orders of magnitude than recomputing from scratch with the best static algorithm. The experiments also reveal that, although the simple dynamic algorithm we suggest is usually the fastest in practice, other dynamic algorithms proposed in the literature yield better results for specific kinds of test sets. 1
A Fully Dynamic Algorithm for Distributed Shortest Paths
 Theoretical Computer Science
, 2003
"... We propose a fullydynamic distributed algorithm for the allpairs shortest paths problem on general networks with positive real edge weights. If is the number of pairs of nodes changing the distance after a single edge modi cation (insert, delete, weight decrease, or weight increase) then th ..."
Abstract

Cited by 10 (6 self)
 Add to MetaCart
We propose a fullydynamic distributed algorithm for the allpairs shortest paths problem on general networks with positive real edge weights. If is the number of pairs of nodes changing the distance after a single edge modi cation (insert, delete, weight decrease, or weight increase) then the message complexity of the proposed algorithm is O(n ) in the worst case, where n is the number of nodes of the network.
Dynamic shortest paths and transitive closure: algorithmic techniques and data structures
 J. Discr. Algor
, 2006
"... In this paper, we survey fully dynamic algorithms for path problems on general directed graphs. In particular, we consider two fundamental problems: dynamic transitive closure and dynamic shortest paths. Although research on these problems spans over more than three decades, in the last couple of ye ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
In this paper, we survey fully dynamic algorithms for path problems on general directed graphs. In particular, we consider two fundamental problems: dynamic transitive closure and dynamic shortest paths. Although research on these problems spans over more than three decades, in the last couple of years many novel algorithmic techniques have been proposed. In this survey, we will make a special effort to abstract some combinatorial and algebraic properties, and some common datastructural tools that are at the base of those techniques. This will help us try to present some of the newest results in a unifying framework so that they can be better understood and deployed also by nonspecialists.
Incremental heuristic search in artificial intelligence
 Artificial Intelligence Magazine
"... Incremental search reuses information from previous searches to find solutions to a series of similar search problems potentially faster than is possible by solving each search problem from scratch. This is important since many artificial intelligence systems have to adapt their plans continuously t ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
Incremental search reuses information from previous searches to find solutions to a series of similar search problems potentially faster than is possible by solving each search problem from scratch. This is important since many artificial intelligence systems have to adapt their plans continuously to changes in (their knowledge of) the world. In this article, we therefore give an overview of incremental search, focusing on Lifelong Planning A*, and outline some of its possible applications in artificial intelligence. Overview It is often important that searches be fast. Artificial intelligence has developed several ways of speeding up searches by trading off the search time and the cost of the resulting path. This includes using inadmissible heuristics (Pohl
CPbased Lagrangian Relaxation for a Multimedia Application
 In [17
, 2001
"... Whereas CP methods are strong with respect to the detection of local infeasibilities, OR approaches have powerful optimization abilities that ground on tight global bounds on the objective. An integration of propagation ideas from CP and Lagrangian relaxation techniques from OR combines the meri ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
Whereas CP methods are strong with respect to the detection of local infeasibilities, OR approaches have powerful optimization abilities that ground on tight global bounds on the objective. An integration of propagation ideas from CP and Lagrangian relaxation techniques from OR combines the merits of both approaches. We introduce a general way of how linear optimization constraints can strengthen their propagation abilities via Lagrangian relaxation. The algorithm is evaluated on a set of benchmark problems stemming from a multimedia application.
Maintaining Longest Paths Incrementally
, 2003
"... Modeling and programming tools for neighborhood search often support invariants, i.e., data structures specified declaratively and automatically maintained incrementally under changes. This paper considers invariants for longest paths in directed acyclic graphs, a fundamental abstraction for man ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
Modeling and programming tools for neighborhood search often support invariants, i.e., data structures specified declaratively and automatically maintained incrementally under changes. This paper considers invariants for longest paths in directed acyclic graphs, a fundamental abstraction for many applications. It presents bounded incremental algorithms for arc insertion and deletion which run in O(###log###) and O(###) respectively, where is a measure of the change in the input and output. The paper also shows how to generalize the algorithm to various classes of multiple insertions/deletions encountered in scheduling applications. Preliminary experimental results show that the algorithms behave well in practice.
Dynamic Shortest Paths Containers
, 2003
"... Using a set of geometric containers to speed up shortest path queries in a weighted graph has been proven a useful tool for dealing with large sparse graphs. Given a layout of a graph G = (V, E), we store, for each edge (u, v) E, the bounding box of all nodes t V for which a shortest utpath ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
Using a set of geometric containers to speed up shortest path queries in a weighted graph has been proven a useful tool for dealing with large sparse graphs. Given a layout of a graph G = (V, E), we store, for each edge (u, v) E, the bounding box of all nodes t V for which a shortest utpath starts with (u, v). Shortest path queries can then be answered by Dijkstra's algorithm restricted to edges where the corresponding bounding box contains the target. In this
Improved Bounds and New TradeOffs for Dynamic All Pairs Shortest Paths
"... Let G be a directed graph with n vertices, subject to dynamic updates, and such that each edge weight can assume at most S different arbitrary real values throughout the sequence of updates. We present a new algorithm for maintaining all pairs shortest paths in G in O(S n) amortized time p ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
Let G be a directed graph with n vertices, subject to dynamic updates, and such that each edge weight can assume at most S different arbitrary real values throughout the sequence of updates. We present a new algorithm for maintaining all pairs shortest paths in G in O(S n) amortized time per update and in O(1) worstcase time per distance query. This improves over previous bounds. We also show how to obtain query/update tradeoffs for this problem, by introducing two new families of algorithms. Algorithms in the first family achieve an update bound of e O(S \Delta k \Delta n and a query bound of e O(n=k), and improve over the best known update bounds for k in the range (n=S) . Algorithms in the second family achieve an update e O e O(n ), and are competitive with the best known update bounds (first family included) for k in the range (n=S) k ! .
An Experimental Study of Dynamic Algorithms for Transitive Closure
 ACM JOURNAL OF EXPERIMENTAL ALGORITHMICS
, 2000
"... We perform an extensive experimental study of several dynamic algorithms for transitive closure. In particular, we implemented algorithms given by Italiano, Yellin, Cicerone et al., and two recent randomized algorithms by Henzinger and King. We propose a netuned version of Italiano's algorithms ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
We perform an extensive experimental study of several dynamic algorithms for transitive closure. In particular, we implemented algorithms given by Italiano, Yellin, Cicerone et al., and two recent randomized algorithms by Henzinger and King. We propose a netuned version of Italiano's algorithms as well as a new variant of them, both of which were always faster than any of the other implementations of the dynamic algorithms. We also considered simpleminded algorithms that were easy to implement and likely to be fast in practice. We tested and compared the above implementations on random inputs, on nonrandom inputs that are worstcase inputs for the dynamic algorithms, and on an input motivated by a realworld graph.
Averagecase analysis of online topological ordering
 of Lecture Notes in Computer Science
, 2007
"... Many applications like pointer analysis and incremental compilation require maintaining a topological ordering of the nodes of a directed acyclic graph (DAG) under dynamic updates. All known algorithms for this problem are either only analyzed for worstcase insertion sequences or only evaluated exp ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
Many applications like pointer analysis and incremental compilation require maintaining a topological ordering of the nodes of a directed acyclic graph (DAG) under dynamic updates. All known algorithms for this problem are either only analyzed for worstcase insertion sequences or only evaluated experimentally on random DAGs. We present the first averagecase analysis of online topological ordering algorithms. We prove an expected runtime of O(n 2 polylog(n)) under insertion of the edges of a complete DAG in a random order for the algorithms of Alpern et