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35
Finding timedependent shortest paths over large graphs
 In Proc. EDBT
, 2008
"... The spatial and temporal databases have been studied widely and intensively over years. In this paper, we study how to answer queries of finding the best departure time that minimizes the total travel time from a place to another, over a road network, where the traffic conditions dynamically change ..."
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Cited by 20 (0 self)
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The spatial and temporal databases have been studied widely and intensively over years. In this paper, we study how to answer queries of finding the best departure time that minimizes the total travel time from a place to another, over a road network, where the traffic conditions dynamically change from time to time. We study a generalized form of this problem, called the timedependent shortestpath problem. A timedependent graph GT is a graph that has an edgedelay function, wi,j(t), associated with each edge (vi, vj), to be stored in a database. The edgedelay function wi,j(t) specifies how much time it takes to travel from node vi to node vj, if it departs from vi at time t. A userspecified query is to ask the minimumtraveltime path, from a source node, vs, to a destination node, ve, over the timedependent graph, GT, with the best departure time to be selected from a time interval T. We denote this user query as LTT(vs, ve, T) over GT. The challenge of this problem is the added complexity due to the time dependency in the timedependent graph. That is, edge delays are not constants, and can vary from time to time. In this paper, we propose a novel algorithm to find the minimumtraveltime path with the best departure time for a LTT(vs, ve, T) query over a large graph GT. Our approach outperforms existing algorithms in terms of both time complexity in theory and efficiency in practice. We will discuss the design of our algorithm, together with its correctness and complexity. We conducted extensive experimental studies over large graphs and will report our findings. 1.
Adaptive fastest path computation on a road network: A traffic mining approach
 In Proc. 2007 Int. Conf. on Very Large Data Bases (VLDB’07
, 2007
"... 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 m ..."
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Cited by 19 (2 self)
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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 distancebased 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 precomputation 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 wellsupported) routes, and that it is significantly faster than competing methods.
Speeding up dynamic shortest path algorithms
 AT&T labs Research Technical Report, TD5RJ8B, Florham Park, NJ
, 2003
"... doi 10.1287/ijoc.1070.0231 ..."
RKleene: A HighPerformance DivideandConquer Algorithm for the AllPair Shortest Path for Densely Connected Networks
, 2007
"... We propose a novel divideandconquer algorithm for the solution of the allpair shortestpath problem for directed and dense graphs with no negative cycles. We propose RKleene, a compact and inplace recursive algorithm inspired by Kleene’s algorithm. RKleene delivers a better performance than p ..."
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Cited by 10 (0 self)
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We propose a novel divideandconquer algorithm for the solution of the allpair shortestpath problem for directed and dense graphs with no negative cycles. We propose RKleene, a compact and inplace recursive algorithm inspired by Kleene’s algorithm. RKleene 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 RKleene, 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.
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 ..."
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Cited by 9 (1 self)
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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.
A Continuous Query System for Dynamic Route Planning
"... 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 ..."
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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 – Kpaths 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.
Discovering Correlated SpatioTemporal Changes in Evolving Graphs
 UNDER CONSIDERATION FOR PUBLICATION IN KNOWLEDGE AND INFORMATION SYSTEMS
, 2007
"... 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 ..."
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Cited by 5 (0 self)
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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 spatiotemporal 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, reallife 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.
The Preliminary Design and Implementation of the Maestro Network Control Platform
, 2008
"... Network operation is inherently complex because it consists of many functions such as routing, firewalling, VPN provisioning, traffic loadbalancing, network maintenance, etc. To cope with this, network designers have created modular components to handle each function. Unfortunately, in reality, una ..."
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Cited by 4 (0 self)
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Network operation is inherently complex because it consists of many functions such as routing, firewalling, VPN provisioning, traffic loadbalancing, 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 cleanlate 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
Replacement Paths via Fast Matrix Multiplication
"... Abstract. Let G = (V, E) be a directed edgeweighted 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 stot path that avoids e. Apart from approximation algorithms and algorithms for special graph classes, the na ..."
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Abstract. Let G = (V, E) be a directed edgeweighted 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 stot 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 stot 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 nvertex graph with integral edgelengths 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 subcubic 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 subquadratic time and returns the length of the shortest utov path that avoids the edge e. In fact, for any constant number of edge failures, we construct a data structure in subcubic time, that answer queries in subquadratic time. Our results also apply for avoiding vertices rather than edges. 1
Algorithmic techniques for maintaining shortest routes in dynamic networks
 Electronic Notes in Theoretical Computer Science
"... 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 combinato ..."
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Cited by 3 (0 self)
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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 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. Key words: Dynamic networks, dynamic graph problems, dynamic shortest paths. 1