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59
Shortestpath and minimumdelay algorithms in networks with timedependent edgelength
 Journal of the ACM
, 1990
"... We consider in this paper the shortestpath problem in networks in which the delay (or weight) of the edges changes with time according to arbitrary functions. We present algorithms for finding the shortestpath and minimumdelay under various waiting constraints and investigate the properties of th ..."
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Cited by 91 (6 self)
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We consider in this paper the shortestpath problem in networks in which the delay (or weight) of the edges changes with time according to arbitrary functions. We present algorithms for finding the shortestpath and minimumdelay under various waiting constraints and investigate the properties of the derived path. We show that if departure time from the source node is unrestricted then a shortest path can be found that is simple and achieves a delay as short as the most unrestricted path. In the case of restricted transit, it is shown that there exist cases where the minimum delay is finite but the path that achieves it is infinite.
SEMIRING FRAMEWORKS AND ALGORITHMS FOR SHORTESTDISTANCE PROBLEMS
, 2002
"... We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorit ..."
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Cited by 73 (20 self)
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We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorithm can be used to solve efficiently classical shortest paths problems or to find the kshortest distances in a directed graph. It can be used to solve singlesource shortestdistance problems in weighted directed acyclic graphs over any semiring. We examine several semirings and describe some specific instances of our generic algorithms to illustrate their use and compare them with existing methods and algorithms. The proof of the soundness of all algorithms is given in detail, including their pseudocode and a full analysis of their running time complexity.
TimeExpanded Graphs for FlowDependent Transit Times
 Proc. 10th Annual European Symposium on Algorithms
, 2002
"... Motivated by applications in road tra#c control, we study flows in networks featuring special characteristics. Firstly, there are transit times on the arcs of the network which specify the amount of time it takes for flow to travel through an arc; in particular, flow values on arcs may change over t ..."
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Cited by 17 (3 self)
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Motivated by applications in road tra#c control, we study flows in networks featuring special characteristics. Firstly, there are transit times on the arcs of the network which specify the amount of time it takes for flow to travel through an arc; in particular, flow values on arcs may change over time. Secondly, the transit time of an arc varies with the current amount of flow using this arc. The latter feature is crucial for various reallife applications; yet, it dramatically increases the degree of di#culty of the resulting optimization problems. While almost all flow problems with constant transit times on the arcs can be solved e#ciently by applying classical (static) flow algorithms in a corresponding timeexpanded network, no such approach was known for flowdependent transit times, up to now. One main contribution of this paper is a timeexpanded network with flowdependent transit times to which the whole algorithmic toolbox developed for static flows can be applied. Although this approach does not entirely capture the behavior of flows over time with flowdependent transit times, we present approximation results which provide evidence of its surprising quality.
Minimum Cost Flows over Time without Intermediate Storage
 In Proceedings of the 14th Annual ACM–SIAM Symposium on Discrete Algorithms
, 2002
"... Flows over time (also called dynamic flows) generalize standard network flows by introducing an element of time. They naturally model problems where travel and transmission are not instantaneous. Solving these problems raises issues that do not arise in standard network flows. One issue is the quest ..."
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Cited by 14 (5 self)
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Flows over time (also called dynamic flows) generalize standard network flows by introducing an element of time. They naturally model problems where travel and transmission are not instantaneous. Solving these problems raises issues that do not arise in standard network flows. One issue is the question of storage of flow at intermediate nodes. In most applications (such as, e. g., traffic routing, evacuation planning, telecommunications etc.), intermediate storage is limited, undesired, or prohibited.
Implicit flow maximization by iterative squaring
"... Application areas like logic design and network analysis produce large graphs G = (V, E) on which traditional algorithms, which work on adjacency list representations, are not practicable anymore. These large graphs often contain regular structures that enable compact implicit representations by dec ..."
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Cited by 13 (9 self)
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Application areas like logic design and network analysis produce large graphs G = (V, E) on which traditional algorithms, which work on adjacency list representations, are not practicable anymore. These large graphs often contain regular structures that enable compact implicit representations by decision diagrams like OBDDs [2, 3, 17]. To solve problems on such implicitly given graphs, specialized algorithms are needed. These are considered as heuristics with typically higher worstcase runtimes than traditional methods. In this paper, an implicit algorithm for flow maximization in 0–1 networks is presented, which works on OBDDrepresentations of node and edge sets. Because it belongs to the class of layerednetwork methods, it has to construct blockingflows. In contrast to previous implicit methods, it avoids breadthfirst searches and layerwise proceeding, and uses iterative squaring instead. In this way, the algorithm needs to execute only O(log 2 V ) operations on the OBDDs to obtain a layerednetwork or at least one augmenting path, respectively. Moreover, each OBDDoperation is efficient if the node and edge sets are represented by compact OBDDs during the flow computation. In order to investigate the algorithm’s behavior on large and structured networks, it has been analyzed on grid networks, on which a maximum flow is computed in polylogarithmic time O(log 3 V ) and space O(log 2 V ). In contrast, previous methods need time and space Ω(V  1/2 log V ) on grids, and are beaten also in experiments for V  ≥ 226.
Applications of Network Optimization
 Network Models, volume 7 of Handbooks in Operations Research and Management Science
, 1995
"... Network optimization has always been a core problem domain in operations research, as well as in computer science, applied mathematics, and many fields of engineering and management. Network optimization problems arise in a variety of situations, and often in situations that apparently are quite unr ..."
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Cited by 13 (0 self)
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Network optimization has always been a core problem domain in operations research, as well as in computer science, applied mathematics, and many fields of engineering and management. Network optimization problems arise in a variety of situations, and often in situations that apparently are quite unrelated to networks. These applications are scattered throughout the literature and until recently no single paper, book, or any other reference, summarized these applications. Consequently, the research and practitioner community has not fully appreciated the richness of these applications. This paper attempts to partially satisfy this important need by presenting a collection of applications of the following fundamental network optimization problems: the shortest path problem, the maximum flow problem, the minimum cost flow problem, assignment and matching problems, and the minimum spanning tree problem. We describe 25 applications of these problems and provide references for more than 100 additional applications. This paper is intended to provide an appreciation for the pervasiveness of network optimization problems. We hope that this paper will stimulate researchers and practitioners to model more decisions problems within the framework of network optimization.
A HyperArc Consistency Algorithm for the Soft Alldierent Constraint
 Principles and Practice of Constraint Programming (CP’2004), volume 3258 of LNCS
, 2004
"... This paper presents an algorithm that achieves hyperarc consistency for the soft alldifferent constraint. To this end, we prove and exploit the equivalence with a minimumcost flow problem. Consistency of the constraint can be checked in O(nm) time, and hyperarc consistency is achieved in O(m) ..."
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Cited by 12 (4 self)
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This paper presents an algorithm that achieves hyperarc consistency for the soft alldifferent constraint. To this end, we prove and exploit the equivalence with a minimumcost flow problem. Consistency of the constraint can be checked in O(nm) time, and hyperarc consistency is achieved in O(m) time, where n is the number of variables involved and m is the sum of the cardinalities of the domains. It improves a previous method that did not ensure hyperarc consistency.
A Linear Programming Formulation of Flows over Time with Piecewise Constant Capacity and Transit Times
, 2003
"... We present an algorithm to solve a deterministic form of a routing problem in delay tolerant networking, in which contact possibilities are known in advance. The algorithm starts with a finite set of contacts with timevarying capacities and transit delays. The output is an optimal schedule assigni ..."
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Cited by 12 (3 self)
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We present an algorithm to solve a deterministic form of a routing problem in delay tolerant networking, in which contact possibilities are known in advance. The algorithm starts with a finite set of contacts with timevarying capacities and transit delays. The output is an optimal schedule assigning messages to edges and times, that respects message priority and minimizes the overall delivery delay. The algorithm consists of two main ingredients: a discretization step in which the raw data provided by the contacts is used to obtain appropriate subdivisions of the relevant time intervals, and a linear program, a dynamic version of the classical multicommodity flow problem, in which transit times are piecewise constant, and where both edges and nodes are capacitated (in the case of edges, with piecewise constant capacities). In fact, we present two equivalent LP formulations, of which one is smaller and runs faster in CPLEX, a general purpose linear solver.