Efficient fastest path computation in the presence of varying speed conditions on a large scale road network is an essential problem in modern navigation systems. Factors affecting road speed, such as weather, time of day, and vehicle type, need to be considered in order to select fast routes that match current driving conditions. Most existing systems compute fastest paths based on road Euclidean distance and a small set of predefined road speeds. However, “History is often the best teacher”. Historical traffic data or driving patterns are often more useful than the simple Euclidean distance-based computation because people must have good reasons to choose these routes, e.g., they may want to avoid those that pass through high crime areas at night or that likely encounter accidents, road construction, or traffic jams. In this paper, we present an adaptive fastest path algorithm capable of efficiently accounting for important driving and speed patterns mined from a large set of traffic data. The algorithm is based on the following observations: (1) The hierarchy of roads can be used to partition the road network into areas, and different path pre-computation strategies can be used at the area level, (2) we can limit our route search strategy to edges and path segments that are actually frequently traveled in the data, and (3) drivers usually traverse the road network through the largest roads available given the distance of the trip, except if there are small roads with a significant speed advantage over the large ones. Through an extensive experimental evaluation on real road networks we show that our algorithm provides desirable (short and well-supported) routes, and that it is significantly faster than competing methods.

Dynamic shortest path algorithms update the shortest paths to take into account a change in an edge weight. This paper describes a new technique that allows the reduction of heap sizes used by several dynamic shortest path algorithms. For unit weight change, the updates can be done without heaps. These reductions almost always reduce the computational times for these algorithms. In computational testing, several dynamic shortest path algorithms with and without the heap-reduction technique are compared. Speedups of up to a factor of 1.8 were observed using the heap-reduction technique on random weight changes and of over a factor of five on unit weight changes. We compare as well with Dijkstra 's algorithm, which recomputes the paths from scratch. With respect to Dijkstra's algorithm, speedups of up to five orders of magnitude are observed. 1.

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 data-structural 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 non-specialists.

We propose a novel divide-and-conquer algorithm for the solution of the all-pair shortest-path problem for directed and dense graphs with no negative cycles. We propose R-Kleene, a compact and in-place recursive algorithm inspired by Kleene’s algorithm. R-Kleene delivers a better performance than previous algorithms for randomly generated graphs represented by highly dense adjacency matrices, in which the matrix components can have any integer value. We show that R-Kleene, unchanged and without any machine tuning, yields consistently between 1/7 and 1/2 of the peak performance running on five very different uniprocessor systems.

Network operation is inherently complex because it consists of many functions such as routing, firewalling, VPN provisioning, traffic load-balancing, network maintenance, etc. To cope with this, network designers have created modular components to handle each function. Unfortunately, in reality, unavoidable dependencies exist between some of the components and they may interact accidentally. At the same time, some policies are realized by compositions of different components, but the methods of composition are ad hoc and fragile. In other words, there is no single mechanism for systematically governing the interactions between the various components. To address these problems, we propose a clean-late system called Maestro. Maestro is an “operating system ” that orchestrates the network control applications that govern the behavior of a network, and directly controls the underlying network devices. Maestro provides abstractions for the modular implementation of network control applications, and is the first system to address the fundamental problems originating from the concurrent operations of network control applications, namely communication between applications, scheduling of application executions, feedback management, concurrency management, and network state transition management. As the

Abstract. Let G = (V, E) be a directed edge-weighted graph and let P be a shortest path from s to t in G. The replacement paths problem asks to compute, for every edge e on P, the shortest s-to-t path that avoids e. Apart from approximation algorithms and algorithms for special graph classes, the naive solution to this problem – removing each edge e on P one at a time and computing the shortest s-to-t path each time – is surprisingly the only known solution for directed weighted graphs, even when the weights are integrals. In particular, although the related shortest paths problem has benefited from fast matrix multiplication, the replacement paths problem has not, and still required cubic time. For an n-vertex graph with integral edge-lengths in {−M,..., M}, we give a randomized Õ(Mn1+ 2 3 ω) = O(Mn 2.584) time algorithm that uses fast matrix multiplication and is sub-cubic for appropriate values of M. In particular, it runs in Õ(n1+ 2 3 ω) time if the weights are small (positive or negative) integers. We also show how to construct a distance sensitivity oracle in the same time bounds. A query (u, v, e) to this oracle requires sub-quadratic time and returns the length of the shortest u-to-v path that avoids the edge e. In fact, for any constant number of edge failures, we construct a data structure in sub-cubic time, that answer queries in sub-quadratic time. Our results also apply for avoiding vertices rather than edges. 1

Graphs provide powerful abstractions of relational data, and are widely used in fields such as network management, web page analysis and sociology. While many graph representations of data describe dynamic and time evolving relationships, most graph mining work treats graphs as static entities. Our focus in this paper is to discover regions of a graph that are evolving in a similar manner. To discover regions of correlated spatio-temporal change in graphs, we propose an algorithm called cSTAG. Whereas most clustering techniques are designed to find clusters that optimise a single distance measure, cSTAG addresses the problem of finding clusters that optimise both temporal and spatial distance measures simultaneously. We show the effectiveness of cSTAG using a quantitative analysis of accuracy on synthetic data sets, as well as demonstrating its utility on two large, real-life data sets, where one is the routing topology of the Internet, and the other is the dynamic graph of files accessed together on the 1998 World Cup official website.

In this paper, we survey algorithms for shortest paths in dynamic networks. Although research on this problem 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 data-structural 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. Key words: Dynamic networks, dynamic graph problems, dynamic shortest paths. 1

Abstract—In this paper, we address the problem of answering continuous route planning queries over a road network, in the presence of updates to the delay (cost) estimates of links. A simple approach to this problem would be to recompute the best path for all queries on arrival of every delay update. However, such a naive approach scales poorly when there are many users who have requested routes in the system. Instead, we propose two new classes of approximate techniques – K-paths and proximity measures to substantially speed up processing of the set of designated routes specified by continuous route planning queries in the face of incoming traffic delay updates. Our techniques work through a combination of precomputation of likely good paths and by avoiding complete recalculations on every delay update, instead only sending the user new routes when delays change significantly. Based on an experimental evaluation with 7,000 drives from real taxi cabs, we found that the routes delivered by our techniques are within 5 % of the best shortest path and have run times an order of magnitude or less compared to a naive approach. I.

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 e#cient in practice can yield interesting clues to the combinatorial properties of the problem, and eventually lead to new theoretically e#cient algorithms.