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Dynamic Shortest Paths Containers
, 2003
"... Using a set of geometric containers to speed up shortest path queries in a weighted graph has been proven a useful tool for dealing with large sparse graphs. Given a layout of a graph G = (V, E), we store, for each edge (u, v) E, the bounding box of all nodes t V for which a shortest utpath ..."
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Cited by 7 (3 self)
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Using a set of geometric containers to speed up shortest path queries in a weighted graph has been proven a useful tool for dealing with large sparse graphs. Given a layout of a graph G = (V, E), we store, for each edge (u, v) E, the bounding box of all nodes t V for which a shortest utpath starts with (u, v). Shortest path queries can then be answered by Dijkstra's algorithm restricted to edges where the corresponding bounding box contains the target. In this
Fully Dynamic Planarity Testing with Applications
"... The fully dynamic planarity testing problem consists of performing an arbitrary sequence of the following three kinds of operations on a planar graph G: (i) insert an edge if the resultant graph remains planar; (ii) delete an edge; and (iii) test whether an edge could be added to the graph without ..."
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Cited by 6 (0 self)
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The fully dynamic planarity testing problem consists of performing an arbitrary sequence of the following three kinds of operations on a planar graph G: (i) insert an edge if the resultant graph remains planar; (ii) delete an edge; and (iii) test whether an edge could be added to the graph without violating planarity. We show how to support each of the above operations in O(n2=3) time, where n is the number of vertices in the graph. The bound for tests and deletions is worstcase, while the bound for insertions is amortized. This is the first algorithm for this problem with sublinear running time, and it affirmatively answers a question posed in [11]. The same data structure has further applications in maintaining the biconnected and triconnected components of a dynamic planar graph. The time bounds are the same: O(n2=3) worstcase time per edge deletion, O(n2=3) amortized time per edge insertion, and O(n2=3) worstcase time to check whether two vertices are either biconnected or triconnected.
A Practical Temporal Constraint Management System for RealTime Applications
"... Abstract. A temporal constraint management system (TCMS) is a temporal network together with algorithms for managing the constraints in that network over time. This paper presents a practical TCMS, called MYSYSTEM, that efficiently handles the propagation of the kinds of temporal constraints commonl ..."
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Cited by 3 (2 self)
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Abstract. A temporal constraint management system (TCMS) is a temporal network together with algorithms for managing the constraints in that network over time. This paper presents a practical TCMS, called MYSYSTEM, that efficiently handles the propagation of the kinds of temporal constraints commonly found in realtime applications, while providing constanttime access to “allpairs, shortestpath ” information that is extremely useful in many applications. The temporal network in MYSYSTEM includes special timepoints for dealing with the passage of time and eliminating the need for certain common forms of constraint propagation. The constraint propagation algorithm in MYSYSTEM maintains a restricted set of entries in the associated allpairs, shortestpath matrix by incrementally propagating changes to the network either from adding a new constraint or strengthening, weakening or deleting an existing constraint. The paper presents empirical evidence to support the claim that MYSYSTEM is scalable to realtime planning, scheduling and acting applications. 1
Geometric Shortest Path Containers
, 2004
"... In this paper, we consider Dijkstra's algorithm for the single source single target shortest path problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. Due to the size of the graph, preprocessing space requirements can be onl ..."
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Cited by 2 (1 self)
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In this paper, we consider Dijkstra's algorithm for the single source single target shortest path problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. Due to the size of the graph, preprocessing space requirements can be only linear in the number of nodes. We assume that a layout of the graph is given. In the preprocessing, we determine from this layout a geometric object for each edge containing all nodes that can be reached by a shortest path starting with that edge.
A Special Case of the Dynamization Problem for Least Cost Paths
, 1991
"... Given a digraph G = (V; E) and a cost function C : E ! IR, which does not imply negative cost cycles, let us denote by G(ffi) the graph obtained from G by adding to the cost of each edge the positive constant ffi; then we want to compute the cost of the least cost path from a given origin r to each ..."
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Given a digraph G = (V; E) and a cost function C : E ! IR, which does not imply negative cost cycles, let us denote by G(ffi) the graph obtained from G by adding to the cost of each edge the positive constant ffi; then we want to compute the cost of the least cost path from a given origin r to each node v in the graph G(ffi) for different choices of ffi 0, without having to run a least cost path algorithm everytime with a new cost function. Through a preprocessing of the given digraph based on the BellmannFord algorithm, we will be able to obtain in time O((jEj + jV j)) the necessary information to generate a structure that will allow us to answer each query in time O(log), where is defined to be the length of the longest least cost path in the digraph. In particular we will see that the only possible candidates to become least cost paths in a graph G(ffi) are the least cost paths of bounded length in the original graph G; further we will show that finding which of these candidates...
Dynamic Controllability of STNUs • 2 • Luke Hunsberger•
, 2013
"... Agent controlling remote spacecraft Fleets of autonomous spacecraft Business manufacturing processes Medical treatment processes ⇒ Temporal constraints among actions ⇒ Actions with uncertain durations ..."
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Agent controlling remote spacecraft Fleets of autonomous spacecraft Business manufacturing processes Medical treatment processes ⇒ Temporal constraints among actions ⇒ Actions with uncertain durations
© 2000 SpringerVerlag New York Inc. Improved Algorithms for Dynamic Shortest Paths 1
"... Abstract. We describe algorithms for finding shortest paths and distances in outerplanar and planar digraphs that exploit the particular topology of the input graph. An important feature of our algorithms is that they can work in a dynamic environment, where the cost of any edge can be changed or th ..."
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Abstract. We describe algorithms for finding shortest paths and distances in outerplanar and planar digraphs that exploit the particular topology of the input graph. An important feature of our algorithms is that they can work in a dynamic environment, where the cost of any edge can be changed or the edge can be deleted. In the case of outerplanar digraphs, our data structures can be updated after any such change in only logarithmic time. A distance query is also answered in logarithmic time. In the case of planar digraphs, we give an interesting tradeoff between preprocessing, query, and update times depending on the value of a certain topological parameter of the graph. Our results can be extended to nvertex digraphs of genus O(n1−ε) for any ε>0. Key Words.
www.elsevier.com/locate/entcs Dynamic Shortest Paths Containers
"... Using a set of geometric containers to speed up shortest path queries in a weighted graph has been proven a useful tool for dealing with large sparse graphs. Given a layout of a graph G =(V,E), we store, for each edge (u, v) ∈ E, the bounding box of all nodes t ∈ V for which a shortest utpath sta ..."
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Using a set of geometric containers to speed up shortest path queries in a weighted graph has been proven a useful tool for dealing with large sparse graphs. Given a layout of a graph G =(V,E), we store, for each edge (u, v) ∈ E, the bounding box of all nodes t ∈ V for which a shortest utpath starts with (u, v). Shortest path queries can then be answered by Dijkstra’s algorithm restricted to edges where the corresponding bounding box contains the target. In this paper, we present new algorithms as well as an empirical study for the dynamic case of this problem, where edge weights are subject to change and the bounding boxes have to be updated. We evaluate the quality and the time for different update strategies that guarantee correct shortest paths in an interesting application to railway information systems, using realworld data from six European countries. Keywords: