Mattia D'Emidio

Dynamically Maintaining Shortest Path Trees under Batches of Updates

In this paper we focus on dynamic batch algorithms for single source shortest paths in graphs with positive real edge weights. A dynamic algorithm is called batch if it is able to handle graph changes that consist of multiple edge updates at a time, i.e. a batch. We propose a new algorithm to process a decremental batch (containing only delete and weight increase operations), a new algorithm to process an incremental batch (containing only insert and weight decrease operations), and a combination of these algorithms to process arbitrary sequences of incremental and decremental batches. These algorithms are update-sensitive, namely they are efficient w.r.t. to the number of nodes in the shortest paths tree that change the parent and/or the distance from the source as a consequence of the changes.

A speed-up technique for distributed shortest paths computation

We propose a simple and practical speed-up technique, which can be combined with every distance vector routing algorithm based on shortest paths, allowing to reduce the total number of messages sent by that algorithm. We combine the new technique with two algorithms known in the literature: DUAL, which is part of CISCOs widely used EIGRP protocol, and the recent DUST, which has been shown to be very effective on networks with power law node degree distribution. We give experimental evidence that these combinations lead to an important gain in terms of the number of messages sent by DUAL and DUST at the price of a little increase in terms of space occupancy per node.

A loop-free shortest-path routing algorithm for dynamic networks

This work introduces Loop-Free Routing (LFR), a new loop-free distance-vector routing algorithm, which is able to update the shortest paths of a distributed network in fully dynamic scenarios. This work also provides an evaluation based on simulations of LFR and Diffuse Update ALgorithm (DUAL), one of the most popular loop-free distance-vector algorithms, which is part of CISCO@?s widely used Enhanced Interior Gateway Routing Protocol (EIGRP). The simulations are performed on dynamic scenarios based on both real-world and controlled instances. The simulations show that LFR is always the best choice in terms of memory requirements, while in terms of messages sent LFR outperforms DUAL on real-world networks, whereas DUAL is the best choice on controlled scenarios.

Experimental Evaluation of Dynamic Shortest Path Tree Algorithms on Homogeneous Batches

In this paper we focus on dynamic batch algorithms for single-source shortest paths in graphs with positive real edge weights. A dynamic algorithm is called batch if it is able to handle graph changes that consist of multiple edge updates at a time, i.e., a batch. Unfortunately, most of the algorithmic solutions known in the literature for this problem are analyzed with respect to heterogeneous parameters, and this makes unfeasible an effective comparison on a theoretical basis. Thus, for a full comprehension of their actual performance, in the past these solutions have been assessed experimentally. In this paper, we move ahead along this direction, by focusing our attention on homogeneous batches, i.e., either incremental or decremental batches, which model realistic dynamic scenarios like node failures in communication networks and traffic jams in road networks. We provide an extensive experimental study including both the most effective previous batch algorithms and a recently developed one, which was explicitly designed (and was shown to be theoretically efficient) exactly for homogeneous batches. Our work complements previous studies and shows that the various solutions can be consistently ranked on the basis of the type of homogeneous batch and of the underlying network. As a result, we believe it can be helpful in selecting a proper solution depending on the specific application scenario.

Fully dynamic maintenance of arc-flags in road networks

The problem of finding best routes in road networks can be solved by applying Dijkstras shortest paths algorithm. Unfortunately, road networks deriving from real-world applications are huge yielding unsustainable times to compute shortest paths. For this reason, great research efforts have been done to accelerate Dijkstras algorithm on road networks. These efforts have led to the development of a number of speed-up techniques, as for example Arc-Flags, whose aim is to compute additional data in a preprocessing phase in order to accelerate the shortest paths queries in an on-line phase. The main drawback of most of these techniques is that they do not work well in dynamic scenarios. In this paper we propose a new algorithm to update the Arc-Flags of a graph subject to edge weight decrease operations. To check the practical performances of the new algorithm we experimentally analyze it, along with a previously known algorithm for edge weight increase operations, on real-world road networks subject to fully dynamic sequences of operations. Our experiments show a significant speed-up in the updating phase of the Arc-Flags, at the cost of a small space and time overhead in the preprocessing phase.

Fully dynamic update of arc-flags

Best connections in real networks are usually found by applying Dijkstras shortest paths algorithm. Unfortunately, networks deriving from real-world applications are huge, yielding unsustainable times to compute shortest paths. Therefore, considerable research has been conducted in recent years to accelerate Dijkstras algorithm on typical instances of transportation and communication networks, such as road networks. These efforts have led to the development of many so called speed-up techniques, as for example Arc-Flags. The main drawback of many of these techniques, including Arc-Flags, is that they do not work well in the realistic dynamic scenarios where the networks change over time. In this article, we introduce a new data structure, named Road-Signs, which is used to update the Arc-Flags of a graph in fully dynamic scenarios. Road-Signs can be used to compute Arc-Flags, can be efficiently updated and does not require large space consumption for sparse networks. We develop a fully dynamic algorithm for updating Arc-Flags, by updating Road-Signs, each time that a modification occurs on an edge of the network. We show that this algorithm is better than recomputation from scratch of Arc-Flags in terms of the affected parameters of the input, which makes this solution suitable to be efficient in practice. However, it is not better than recomputation from scratch in the worst case. We also propose an experimental study to evaluate the practical performance of the new dynamic algorithm. To this aim, we use real-world road networks subject to sequences of weight change operations. Our experiments show a significant speed-up in the updating phase with respect to the recomputation from scratch of Arc-Flags.Copyright

Explore and repair graphs with black holes using mobile entities

In this paper, we study the problem of mobile entities that synchronously have to explore and repair a graph with faulty nodes, usually called black-holes, that destroy any entering entity. We consider the scenario where the destruction of an entity by means of a black-hole also affects all the entities within a fixed range r (in terms of number of edges), while the black-hole disappears. Clearly, if there are b black-holes in the graph, then k � b entities are necessary to remove all of them from that graph. We ask for the minimum number of synchronous steps needed to make safe all the graph.The results of this paper are both theoretical and experimental, and can be summarized as follows. From the theoretical point of view, first we show that the problem is NP-hard even for b = k = 1 . Then, we provide a general lower bound holding when r � 0 and a higher one for the case of r 0 . We then consider the case of r � 1 . We propose an optimal solution holding when k is unbounded, that is, an infinite number of robots is available. Then, we provide three different exploration strategies, named snake, scout, and parallel-scout, respectively, for the case of bounded k, that is, the number of robots is fixed a priori. The three strategies are then analyzed according to the time complexity with respect to the lower bound. From the experimental point of view, we implemented the three strategies and tested them on different scenarios with the aim of assessing their practical performance. The experiments confirm the theoretical analysis and show that parallel-scout is always by far the best exploration strategy in practice.

Engineering a new loop-free shortest paths routing algorithm

We present LFR (Loop Free Routing), a new loop-free distance vector routing algorithm, which is able to update the shortest paths of a distributed network with n nodes in fully dynamic scenarios. If Φ is the total number of nodes affected by a set of updates to the network, and φ is the maximum number of destinations for which a node is affected, then LFR requires O(Φ ·Δ) messages and O(n+φ ·Δ) space per node, where Δ is the maximum degree of the nodes of the network. We experimentally compare LFR with DUAL, one of the most popular loop-free distance vector algorithms, which is part of CISCOs EIGRP protocol and requires O(Φ ·Δ) messages and Θ(n ·Δ) space per node. The experiments are based on both real-world and artificial instances and show that LFR is always the best choice in terms of memory requirements, while in terms of messages LFR outperforms DUAL on real-world instances, whereas DUAL is the best choice on artificial instances.

Engineering Graph-Based Models for Dynamic Timetable Information Systems

Many efforts have been done in the last years to model public transport timetables in order to find optimal routes. The proposed models can be classified into two types: those representing the timetable as an array, and those representing it as a graph. The array-based models have been shown to be very effective in terms of query time, while the graph-based models usually answer queries by computing shortest paths, and hence they are suitable to be used in combination with speed-up techniques developed for road networks. In this paper, we focus on the dynamic behavior of graph-based models considering the case where transportation systems are subject to delays with respect to the given timetable. We make three contributions: (i) we give a simplified and optimized update routine for the well-known time-expanded model along with an engineered query algorithm; (ii) we propose a new graph-based model tailored for handling dynamic updates; (iii) we assess the effectiveness of the proposed models and algorithms by an experimental study, which shows that both models require negligible update time and a query time which is comparable to that required by some array-based models.

Enhancing the computation of distributed shortest paths on real dynamic networks

The problem of finding and updating shortest paths in distributed networks is considered crucial in todays practical applications. In the recent past, there has been a renewed interest in devising new efficient distance-vector algorithms as an attractive alternative to link-state solutions for large-scale Ethernet networks. In this paper we present Distributed Computation Pruning (DCP), a new technique, which can be combined with every distance-vector algorithm based on shortest paths, allowing to reduce the total number of messages sent by that algorithm and its space occupancy per node. To check its effectiveness, we combined DCP with DUAL (Diffuse Update ALgorithm), one of the most popular distance-vector algorithm in the literature, and with the recently introduced LFR (Loop Free Routing) which has been shown to have good performances on real networks. We give experimental evidence that these combinations lead to a significant gain both in terms of number of messages sent and memory requirements per node.