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MATRIX REPRESENTATIONS AND INDEPENDENCIES IN DIRECTED ACYCLIC GRAPHS
 SUBMITTED TO THE ANNALS OF STATISTICS
, 2008
"... For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorizing according to the given graph. Both criteria are based on special types of path in graphs. They are called separation criteria beca ..."
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For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorizing according to the given graph. Both criteria are based on special types of path in graphs. They are called separation criteria because independence holds whenever the conditioning set is a separating set in a graph theoretical sense. We introduce and discuss an alternative approach using binary matrix representations of graphs in which zeros indicate independence statements. A matrix condition is shown to give a new path criterion for separation and to be equivalent to each of the previous two path criteria.
GRAIL: a scalable index for reachability queries in very large graphs
, 2012
"... Given a large directed graph, rapidly answering reachability queries between source and target nodes is an important problem. Existing methods for reachability tradeoff indexing time and space versus query time performance. However, the biggest limitation of existing methods is that they do not scal ..."
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Cited by 5 (0 self)
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Given a large directed graph, rapidly answering reachability queries between source and target nodes is an important problem. Existing methods for reachability tradeoff indexing time and space versus query time performance. However, the biggest limitation of existing methods is that they do not scale to very large realworld graphs. We present a simple yet scalable reachability index, called GRAIL, that is based on the idea of randomized interval labeling and that can effectively handle very large graphs. Based on an extensive set of experiments, we show that while more sophisticated methods work better on small graphs, GRAIL is the only index that can scale to millions of nodes and edges. GRAIL has linear indexing time and space, and the query time ranges from constant time to being linear in the graph order and size. Our reference C++ implementations are open source and available for download at
On the Complexity of TimeDependent Shortest Paths
"... We investigate the complexity of shortest paths in timedependent graphs, in which the costs of edges vary as a function of time, and as a result the shortest path between two nodes s and d can change over time. Our main result is that when the edge cost functions are (polynomialsize) piecewise line ..."
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We investigate the complexity of shortest paths in timedependent graphs, in which the costs of edges vary as a function of time, and as a result the shortest path between two nodes s and d can change over time. Our main result is that when the edge cost functions are (polynomialsize) piecewise linear, the shortest path from s to d can change Θ(log n) n times, settling a severalyearold conjecture of Dean [Technical Reports, 1999, 2004]. We also show that the complexity is polynomial if the slopes of the linear function come from a restricted class, present an outputsensitive algorithm for the general case, and describe a scheme for a (1 + ɛ)approximation of the travel time function in nearquadratic space. Finally, despite the fact that the arrival time function may have superpolynomial complexity, we show that a minimum delay path for any departure time interval can be computed in polynomial time. 1
Batch Dynamic SingleSource ShortestPath Algorithms: An Experimental Study
, 2009
"... A dynamic shortestpath algorithm is called a batch algorithm if it is able to handle graph changes that consist of multiple edge updates at a time. In this paper we focus on fullydynamic batch algorithms for singlesource shortest paths in directed graphs with positive edge weights. We give an exte ..."
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A dynamic shortestpath algorithm is called a batch algorithm if it is able to handle graph changes that consist of multiple edge updates at a time. In this paper we focus on fullydynamic batch algorithms for singlesource shortest paths in directed graphs with positive edge weights. We give an extensive experimental study of the existing algorithms for the singleedge and the batch case, including a broad set of test instances. We further present tuned variants of the already existing SWSFFPalgorithm being up to 15 times faster than SWSFFP. A surprising outcome of the paper is the astonishing level of data dependency of the algorithms.
A Dynamic Model for Fire Emergency Evacuation Based on Wireless Sensor Networks
"... Abstract — This work introduces a dynamic model for the fire emergency evacuation problem. The model extends the concept safety introduced by Barnes et.al. for the situation when the navigation graph is dynamic. The two possible scenarios are described for using the dynamic model with a Wireless Sen ..."
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Abstract — This work introduces a dynamic model for the fire emergency evacuation problem. The model extends the concept safety introduced by Barnes et.al. for the situation when the navigation graph is dynamic. The two possible scenarios are described for using the dynamic model with a Wireless Sensor Network for fire emergency evacuation.
Proceedings of the Twentieth International Conference on Automated Planning and Scheduling (ICAPS 2010) Incrementally Solving STNs by Enforcing Partial Path Consistency
"... Efficient management and propagation of temporal constraints is important for temporal planning as well as for scheduling. During plan development, new events and temporal constraints are added and existing constraints may be tightened; the consistency of the whole temporal network is frequently che ..."
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Efficient management and propagation of temporal constraints is important for temporal planning as well as for scheduling. During plan development, new events and temporal constraints are added and existing constraints may be tightened; the consistency of the whole temporal network is frequently checked; and results of constraint propagation guide further search. Recent work shows that enforcing partial path consistency provides an efficient means of propagating temporal information for the popular Simple Temporal Network (STN). We show that partial path consistency can be enforced incrementally, thus exploiting the similarities of the constraint network between subsequent edge tightenings. We prove that the worstcase time complexity of our algorithm can be bounded both by the number of edges in the chordal graph (which is better than the previous bound of the number of vertices squared), and by the degree of the chordal graph times the number of vertices incident on updated edges. We show that for many sparse graphs, the latter bound is better than that of the previously bestknown approaches. In addition, our algorithm requires space only linear in the number of edges of the chordal graph, whereas earlier work uses space quadratic in the number of vertices. Finally, empirical results show that when incrementally solving sparse STNs, stemming from problems such as Hierarchical Task Network planning, our approach outperforms extant algorithms. 1.
Distance Oracles for TimeDependent Networks
"... Abstract. We present the first approximate distance oracle for sparse directed networks with timedependent arctraveltimes determined by continuous, piecewise linear, positive functions possessing the FIFO property. Our approach precomputes (1 + ε)−approximate distance summaries from selected la ..."
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Abstract. We present the first approximate distance oracle for sparse directed networks with timedependent arctraveltimes determined by continuous, piecewise linear, positive functions possessing the FIFO property. Our approach precomputes (1 + ε)−approximate distance summaries from selected landmark vertices to all other vertices in the network, and provides two sublineartime query algorithms that deliver constant and (1+σ)−approximate shortesttraveltimes, respectively, for arbitrary origindestination pairs in the network. Our oracle is based only on the sparsity of the network, along with two quite natural assumptions about traveltime functions which allow the smooth transition towards asymmetric and timedependent distance metrics. 1
ECEASST Incremental Pattern Matching for Regular Expressions
"... Abstract: Graph pattern matching lies at the heart of any graph transformationbased system. Incremental pattern matching is one approach proposed for reducing the overall cost of pattern matching over successive transformations by preserving the matches that stay relevant after a rule application. ..."
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Abstract: Graph pattern matching lies at the heart of any graph transformationbased system. Incremental pattern matching is one approach proposed for reducing the overall cost of pattern matching over successive transformations by preserving the matches that stay relevant after a rule application. An important issue in any matching scheme, is the ability to properly and consistently deal with various facilities that add to the expressiveness of a GTtool’s rule language. One such feature is the support for regular path expressions, which would let two nodes to be considered as a “match”, if a certain path of edges exists between them. In this paper, the incorporation of regular expression support into incremental pattern matching is discussed within the context of the GROOVE tool set. This includes laying down a formal foundation for incremental pattern matching for regular expressions which is then used to justify the extension proposed to add regular expression support to a wellknown pattern matching algorithm.