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13
Finding the k Shortest Paths
, 1997
"... We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest pat ..."
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Cited by 290 (1 self)
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We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest paths from a given source s to each vertex in the graph, in total time O(m + n log n +kn). We describe applications to dynamic programming problems including the knapsack problem, sequence alignment, maximum inscribed polygons, and genealogical relationship discovery. 1 Introduction We consider a longstudied generalization of the shortest path problem, in which not one but several short paths must be produced. The k shortest paths problem is to list the k paths connecting a given sourcedestination pair in the digraph with minimum total length. Our techniques also apply to the problem of listing all paths shorter than some given threshhold length. In the version of these problems studi...
Better kbest parsing
, 2005
"... We discuss the relevance of kbest parsing to recent applications in natural language processing, and develop efficient algorithms for kbest trees in the framework of hypergraph parsing. To demonstrate the efficiency, scalability and accuracy of these algorithms, we present experiments on Bikel’s i ..."
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Cited by 147 (16 self)
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We discuss the relevance of kbest parsing to recent applications in natural language processing, and develop efficient algorithms for kbest trees in the framework of hypergraph parsing. To demonstrate the efficiency, scalability and accuracy of these algorithms, we present experiments on Bikel’s implementation of Collins ’ lexicalized PCFG model, and on Chiang’s CFGbased decoder for hierarchical phrasebased translation. We show in particular how the improved output of our algorithms has the potential to improve results from parse reranking systems and other applications. 1
On the Difficulty of Some Shortest Path Problems
, 2003
"... We prove superlinear lower bounds for some shortest path problems in directed graphs, where no such bounds were previously known. The central problem in our study is the replacement paths problem: Given a directed graph G with nonnegative edge weights, and a shortest path P = {e_1, e_2, ..., e_p} ..."
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Cited by 26 (8 self)
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We prove superlinear lower bounds for some shortest path problems in directed graphs, where no such bounds were previously known. The central problem in our study is the replacement paths problem: Given a directed graph G with nonnegative edge weights, and a shortest path P = {e_1, e_2, ..., e_p} between two nodes s and t, compute the shortest path distances from s to t in each of the p graphs obtained from G by deleting one of the edges e_i. We show that the replacement paths problem requires Ω(m√n) time in the worst case whenever m = O(n√n). This also establishes a similar...
Fault Tolerance and Load Balancing in QoS Provisioning with Multiple MPLS Paths
 Lecture Notes in Computer Science, 2092:155–, 2001. International Workshop on Quality of Service (IWQoS
, 2001
"... The paper presents approaches for fault tolerance and load balancing in QoS provisioning using multiple alternate paths. The proposed multiple QoS path computation algorithm searches for maximally disjoint (i.e., minimally overlapped) multiple paths such that the impact of link/node failures bec ..."
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Cited by 17 (6 self)
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The paper presents approaches for fault tolerance and load balancing in QoS provisioning using multiple alternate paths. The proposed multiple QoS path computation algorithm searches for maximally disjoint (i.e., minimally overlapped) multiple paths such that the impact of link/node failures becomes significantly reduced, and the use of multiple paths renders QoS services more robust in unreliable network conditions. The algorithm is not limited to finding fully disjoint paths. It also exploits partially disjoint paths by carefully selecting and retaining common links in order to produce more options. Moreover, it offers the benefits of load balancing in normal operating conditions by deploying appropriate call allocation methods according to traffic characteristics.
Finding the k Shortest Simple Paths: A New Algorithm and its Implementation
"... We describe a new algorithm to enumerate the k shortest simple (loopless) paths in a directed graph and report on its implementation. Our algorithm is based on a replacement paths algorithm proposed recently by Hershberger and Suri [7], and can yield a factor #(n) improvement for this problem. But t ..."
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Cited by 16 (1 self)
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We describe a new algorithm to enumerate the k shortest simple (loopless) paths in a directed graph and report on its implementation. Our algorithm is based on a replacement paths algorithm proposed recently by Hershberger and Suri [7], and can yield a factor #(n) improvement for this problem. But there is a caveat: the fast replacement paths subroutine is known to fail for some directed graphs. However, the failure is easily detected, and so our k shortest paths algorithm optimistically uses the fast subroutine, then switches to a slower but correct algorithm if a failure is detected. Thus the algorithm achieves its #(n) speed advantage only when the optimism is justified. Our empirical results show that the replacement paths failure is a rare phenomenon, and the new algorithm outperforms the current best algorithms; the improvement can be substantial in large graphs. For instance, on GIS map data with about 5000 nodes and 12000 edges, our algorithm is 48 times faster. In synthetic graphs modeling wireless ad hoc networks, our algorithm is about 20 times faster.
Multiple Path QoS Routing
 Proceedings of ICC'01 Finland
, 2001
"... We propose a QoS (Quality of Service) routing scheme in which a connection between a sourcedestination pair can be assigned to one of several alternative paths. The goal of our approach is to compensate for the inaccuracy of the link state information kept at network nodes. Starting from the well k ..."
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Cited by 4 (0 self)
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We propose a QoS (Quality of Service) routing scheme in which a connection between a sourcedestination pair can be assigned to one of several alternative paths. The goal of our approach is to compensate for the inaccuracy of the link state information kept at network nodes. Starting from the well known algorithm by Dijkstra, we develop a collection of Kshortest path routing strategies and investigate their performance under a diverse set of network topologies and traffic conditions. We demonstrate that Kshortest path routing offers a lower blocking probability and more balanced link utilization than traditional schemes based on a single shortest path. Consequently, our approach makes it possible to reduce the frequency of link state exchange, and the incurred bandwidth overhead, without sacrificing the overall performance of the network.
M best solutions over Graphical Models
 In CRAGS10 Workshop
, 2010
"... Abstract. Bucket elimination is an algorithmic framework that generalizes dynamic programming to accommodate many problemsolving and reasoning tasks. In particular, it can be used for any combinatorial optimization task such as finding most probable configurations in a Bayesian network. In this pap ..."
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Cited by 3 (1 self)
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Abstract. Bucket elimination is an algorithmic framework that generalizes dynamic programming to accommodate many problemsolving and reasoning tasks. In particular, it can be used for any combinatorial optimization task such as finding most probable configurations in a Bayesian network. In this paper we present a new algorithm elimmopt, extending bucket elimination for the task of finding m best solutions for an optimization task for any value of m. We formulate our algorithm using general notion of combination and marginalization operators and show that our approach is sound. We provide complexity analysis and compare it with related work. Potential extension to the minibucket framework and its impact on heuristicsearch for mbest are discussed.
Traffic engineering techniques and algorithms for the internet. Tech report, Rensselear Polytechnic Inst
, 2002
"... Traffic engineering broadly relates to optimization of the operational performance of a network. This survey discusses techniques like multipath routing, traffic splitting, constraintbased routing, pathprotection etc. that are used for traffic engineering in contemporary Internet Service Provider ..."
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Cited by 2 (0 self)
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Traffic engineering broadly relates to optimization of the operational performance of a network. This survey discusses techniques like multipath routing, traffic splitting, constraintbased routing, pathprotection etc. that are used for traffic engineering in contemporary Internet Service Provider (ISP) networks. These techniques can be classified under two broad classes, connectionless and connectionoriented, that dominate the current debate on nextgeneration routing and traffic engineering in IP networks. The connectionless approach evolves current distancevector and linkstate algorithms, or influences routing metrics. The connectionoriented approach uses signaling and is being used by techniques like Multi Protocol Label Switching (MPLS). Connectionoriented techniques offer a convenient way to monitor, allocate, reroute, and protect resources for a given traffic on an explicit and flexible basis. This survey will examine the core problems, discuss solutions in both connectionless and signaled approach, and point to topics for research and advanced development.
Using kshortest paths algorithms to accommodate user preferences in the optimization of public transport travel
 Proceeding of UKSIM 2004
, 2004
"... Abstract: Traffic congestion is becoming a serious problem in more and more modern cities. Encouraging more privatevehicle drivers to use public transportation is one of the most effective and economical ways to reduce the ever increasing congestion problem on the streets (Hartley and Bargiela, 200 ..."
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Cited by 1 (0 self)
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Abstract: Traffic congestion is becoming a serious problem in more and more modern cities. Encouraging more privatevehicle drivers to use public transportation is one of the most effective and economical ways to reduce the ever increasing congestion problem on the streets (Hartley and Bargiela, 2001). To make public transport services more attractive and competitive, providing travellers with individual travel advice for journeys becomes crucial. However, with the massive and complex network of a modern city, finding one or several suitable route(s) according to user preferences from one place to another is not a simple task. In this paper, the author presents an approach that uses Kshortest paths algorithms to compute a reasonable number of ranked shortest paths, with the ultimate ‘most optimal ’ path being selected by consideration of the preferences. Some experiments have been done based on the public transportation network of Nottingham City. Keywords: User preferences, Kshortest paths algorithms, Multiobjective algorithms 1.