GraphStream: A Tool for bridging the gap between Complex Systems and Dynamic Graphs

The notion of complex systems is common to many domains, from Biology to Economy, Computer Science, Physics, etc. Often, these systems are made of sets of entities moving in an evolving environment. One of their major characteristics is the emergence of some global properties stemmed from local interactions between the entities themselves and between the entities and the environment. The structure of these systems as sets of interacting entities leads researchers to model them as graphs. However, their understanding requires most often to consider the dynamics of their evolution. It is indeed not relevant to study some properties out of any temporal consideration. Thus, dynamic graphs seem to be a very suitable model for investigating the emergence and the conservation of some properties. GraphStream is a Java-based library whose main purpose is to help researchers and developers in their daily tasks of dynamic problem modeling and of classical graph management tasks: creation, processing, display, etc. It may also be used, and is indeed already used, for teaching purpose. GraphStream relies on an event-based engine allowing several event sources. Events may be included in the core of the application, read from a file or received from an event handler

Fully dynamic all-pairs shortest paths with worst-case update-time revisited

We revisit the classic problem of dynamically maintaining shortest paths between all pairs of nodes of a directed weighted graph. The allowed updates are insertions and deletions of nodes and their incident edges. We give worst-case guarantees on the time needed to process a single update (in contrast to related results, the update time is not amortized over a sequence of updates). Our main result is a simple randomized algorithm that for any parameter $c>1$ has a worst-case update time of $O(cn^{2+2/3} \log^{4/3}{n})$ and answers distance queries correctly with probability $1-1/n^c$, against an adaptive online adversary if the graph contains no negative cycle. The best deterministic algorithm is by Thorup [STOC 2005] with a worst-case update time of $\tilde O(n^{2+3/4})$ and assumes non-negative weights. This is the first improvement for this problem for more than a decade. Conceptually, our algorithm shows that randomization along with a more direct approach can provide better bounds.Comment: To be presented at the Symposium on Discrete Algorithms (SODA) 201

Route planning based on uncertain information in transport networks

The goal of this paper is to find a solution for route planning in a transport network where the network type can be arbitrary: a network of bus routes, a network of tram rails, a road network or any other type of a transport network. Furthermore, the costs of network elements are uncertain. The concept is based on the Dempster–Shafer theory and Dijkstra's algorithm which helps with finding the best routes. The paper focuses on conventional studies without considering traffic accidents or other exceptional circumstances. The concept is presented by an undirected graph. In order to model conventional real transport, the influencing factors of traffic congestion have been applied in the abstract model using uncertain probabilities described by probability intervals. On the basis of these intervals, the cost intervals of each road can be calculated. Taking into account the uncertain values of costs, an algorithm has been outlined for determining the best routes from one node to all other nodes comparing cost intervals and using decision rules that can be defined by the end user, and if necessary, node by node. The suggested solution can be applied for both one type of network as well as for a combination of a few of those

Fully Dynamic All Pairs Shortest Paths with Real Edge Weights

We present the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with real-valued edge weights. Given a dynamic directed graph G such that each edge can assume at most S di#erent real values, we show how to support updates in O(n amortized time and queries in optimal worst-case time. No previous fully dynamic algorithm was known for this problem. In the special case where edge weights can only be increased, we give a randomized algorithm with one-sided error which supports updates faster in O(S We also show how to obtain query/update trade-o#s for this problem, by introducing two new families of algorithms. Algorithms in the first family achieve an update bound of O(n/k), and improve over the best known update bounds for k in the . Algorithms in the second family achieve an update bound of ), and are competitive with the best known update bounds (first family included) for k in the range (n/S) # Work partially supported by the IST Programme of the EU under contract n. IST-199914. 186 (ALCOM-FT) and by CNR, the Italian National Research Council, under contract n. 01.00690.CT26. Portions of this work have been presented at the 42nd Annual Symp. on Foundations of Computer Science (FOCS 2001) [8] and at the 29th International Colloquium on Automata, Languages, and Programming (ICALP'02) [9]

Fully dynamic all pairs shortest paths with real edge weights

We present the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with real-valued edge weights. Given a dynamic directed graph G such that each edge can assume at most S different real values, we show how to support updates in O(n(2.5)root/S log(3) n) amortized time and queries in optimal worst-case time. This algorithm is deterministic: no previous fully dynamic algorithm was known before for this problem. In the special case where edge weights can only be increased, we give a randomized algorithm with one-sided error that supports updates faster in O (S . n log(3) n) amortized time. We also show how to obtain query/update trade-offs for this problem, by introducing two new families of randomized algorithms. Algorithms in the first family achieve an update bound of (O) over tilde (S . k . n(2))(1) and a query bound of (O) over tilde (n/k), and improve over the previous best known update bounds for k in the range (n/S)(1/3) (S . k . n(2)) and a query bound of (O) over tilde (n(2)/k(2)), and are competitive with the previous best known update bounds (first family included) for k in the range (n/S)(1/6) <= k < (n/S)(1/3). (C) 2006 Elsevier Inc. All rights reserved

Fully Dynamic All-pairs Shortest Paths with Worst-case Update-time revisited

We revisit the classic problem of dynamically maintaining shortest paths between all pairs of nodes of a directed weighted graph. The allowed updates are insertions and deletions of nodes and their incident edges. We give worst-case guarantees on the time needed to process a single update (in contrast to related results, the update time is not amortized over a sequence of updates). Our main result is a simple randomized algorithm that for any parameter $c>1$ has a worst-case update time of $O(cn^{2+2/3} \log^{4/3}{n})$ and answers distance queries correctly with probability $1-1/n^c$, against an adaptive online adversary if the graph contains no negative cycle. The best deterministic algorithm is by Thorup [STOC 2005] with a worst-case update time of $\tilde O(n^{2+3/4})$ and assumes non-negative weights. This is the first improvement for this problem for more than a decade. Conceptually, our algorithm shows that randomization along with a more direct approach can provide better bounds