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61
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...
Vickrey Prices and Shortest Paths: What is an edge worth?
 In Proceedings of the 42nd Symposium on the Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos
, 2001
"... We solve a shortest path problem that is motivated by recent interest in pricing networks or other computational resources. Informally, how much is an edge in a network worth to a user who wants to send data between two nodes along a shortest path? If the network is a decentralized entity, such as t ..."
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Cited by 96 (5 self)
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We solve a shortest path problem that is motivated by recent interest in pricing networks or other computational resources. Informally, how much is an edge in a network worth to a user who wants to send data between two nodes along a shortest path? If the network is a decentralized entity, such as the Internet, in which multiple selfinterested agents own different parts of the network, then auctionbased pricing seems appropriate. A celebrated result from auction theory shows that the use of Vickrey pricing motivates the owners of the network resources to bid truthfully. In Vickrey's scheme, each agent is compensated in proportion to the marginal utility he brings to the auction. In the context of shortest path routing, an edge's utility is the value by which it lowers the length of the shortest paththe difference between the shortest path lengths with and without the edge. Our problem is to compute these marginal values for all the edges of the network efficiently. The na ve method requires solving the singlesource shortest path problem up to n times, for an nnode network. We show that the Vickrey prices for all the edges can be computed in the same asymptotic time complexity as one singlesource shortest path problem. This solves an open problem posed by Nisan and Ronen [12]. 1.
Ambivalent Data Structures For Dynamic 2EdgeConnectivity And k Smallest Spanning Trees
 SIAM J. Comput
, 1991
"... . Ambivalent data structures are presented for several problems on undirected graphs. These data structures are used in finding the k smallest spanning trees of a weighted undirected graph in O(m log #(m, n) + min{k 3/2 ,km 1/2 }) time, where m is the number of edges and n the number of vertice ..."
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Cited by 83 (1 self)
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. Ambivalent data structures are presented for several problems on undirected graphs. These data structures are used in finding the k smallest spanning trees of a weighted undirected graph in O(m log #(m, n) + min{k 3/2 ,km 1/2 }) time, where m is the number of edges and n the number of vertices in the graph. The techniques are extended to find the k smallest spanning trees in an embedded planar graph in O(n + k(log n) 3 ) time. Ambivalent data structures are also used to dynamically maintain 2edgeconnectivity information. Edges and vertices can be inserted or deleted in O(m 1/2 ) time, and a query as to whether two vertices are in the same 2edgeconnected component can be answered in O(log n) time, where m and n are understood to be the current number of edges and vertices, respectively. Key words. analysis of algorithms, data structures, embedded planar graph, fully persistent data structures, k smallest spanning trees, minimum spanning tree, online updating, topology tr...
Finding and approximating topk answers in keyword proximity search
 In PODS
, 2006
"... Various approaches for keyword proximity search have been implemented in relational databases, XML and the Web. Yet, in all of them, an answer is a Qfragment, namely, a subtree T of the given data graph G, such that T contains all the keywords of the query Q and has no proper subtree with this prop ..."
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Cited by 43 (4 self)
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Various approaches for keyword proximity search have been implemented in relational databases, XML and the Web. Yet, in all of them, an answer is a Qfragment, namely, a subtree T of the given data graph G, such that T contains all the keywords of the query Q and has no proper subtree with this property. The rank of an answer is inversely proportional to its weight. Three problems are of interest: finding an optimal (i.e., topranked) answer, computing the topk answers and enumerating all the answers in ranked order. It is shown that, under data complexity, an efficient algorithm for solving the first problem is sufficient for solving the other two problems with polynomial delay. Similarly, an efficient algorithm for finding a θapproximation of the optimal answer suffices for carrying out the following two tasks with polynomial delay, under queryanddata complexity. First, enumerating in a (θ + 1)approximate order. Second, computing a (θ + 1)approximation of the topk answers. As a corollary, this paper gives the first efficient algorithms, under data complexity, for enumerating all the answers in ranked order and for computing the topk answers. It also gives the first efficient algorithms, under queryanddata complexity, for enumerating in a provably approximate order and for computing an approximation of the topk answers.
Combinatorial algorithms for DNA sequence assembly
 Algorithmica
, 1993
"... The trend towards very large DNA sequencing projects, such as those being undertaken as part of the human genome initiative, necessitates the development of efficient and precise algorithms for assembling a long DNA sequence from the fragments obtained by shotgun sequencing or other methods. The seq ..."
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Cited by 42 (3 self)
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The trend towards very large DNA sequencing projects, such as those being undertaken as part of the human genome initiative, necessitates the development of efficient and precise algorithms for assembling a long DNA sequence from the fragments obtained by shotgun sequencing or other methods. The sequence reconstruction problem that we take as our formulation of DNA sequence assembly is a variation of the shortest common superstring problem, complicated by the presence of sequencing errors and reverse complements of fragments. Since the simpler superstring problem is NPhard, any efficient reconstruction procedure must resort to heuristics. In this paper, however, a four phase approach based on rigorous design criteria is presented, and has been found to be very accurate in practice. Our method is robust in the sense that it can accommodate high sequencing error rates and list a series of alternate solutions in the event that several appear equally good. Moreover it uses a limited form ...
Efficient Precomputation of QualityofService Routes
, 1998
"... Qualityofservice (QoS) routing satisfies application performance requirements and improves network resource usage by selecting paths based on connection traffic parameters and available link capacity. However, QoSrouting protocols can introduce significant network overhead for computing routes an ..."
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Cited by 41 (4 self)
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Qualityofservice (QoS) routing satisfies application performance requirements and improves network resource usage by selecting paths based on connection traffic parameters and available link capacity. However, QoSrouting protocols can introduce significant network overhead for computing routes and distributing information about link load. Route precomputation is an effective way to amortize the cost of the path selection algorithm over multiple connection requests. This paper introduces efficient mechanisms for precomputing one or moreroutes to each destination, and on demand checking of the suitability of the routes at connection arrival, based on the most recent linkstate information. Simulation experiments show that the route precomputation and route extraction techniques are effective at lowering the computational overheads for QoS routing, while achieving performance similar to the more expensive ondemand pathselection schemes.
ShortestPath Kernels on Graphs
 In Proceedings of the 2005 International Conference on Data Mining
, 2005
"... Data mining algorithms are facing the challenge to deal with an increasing number of complex objects. For graph data, a whole toolbox of data mining algorithms becomes available by defining a kernel function on instances of graphs. Graph kernels based on walks, subtrees and cycles in graphs have bee ..."
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Cited by 35 (5 self)
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Data mining algorithms are facing the challenge to deal with an increasing number of complex objects. For graph data, a whole toolbox of data mining algorithms becomes available by defining a kernel function on instances of graphs. Graph kernels based on walks, subtrees and cycles in graphs have been proposed so far. As a general problem, these kernels are either computationally expensive or limited in their expressiveness. We try to overcome this problem by defining expressive graph kernels which are based on paths. As the computation of all paths and longest paths in a graph is NPhard, we propose graph kernels based on shortest paths. These kernels are computable in polynomial time, retain expressivity and are still positive definite. In experiments on classification of graph models of proteins, our shortestpath kernels show significantly higher classification accuracy than walkbased kernels. 1
Building realistic mobility models from coarsegrained traces
 in Proc. MobiSys
, 2006
"... In this paper we present a tracedriven framework capable of building realistic mobility models for the simulation studies of mobile systems. With the goal of realism, this framework combines coarsegrained wireless traces, i.e., association data between WiFi users and access points, with an actual ..."
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Cited by 31 (5 self)
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In this paper we present a tracedriven framework capable of building realistic mobility models for the simulation studies of mobile systems. With the goal of realism, this framework combines coarsegrained wireless traces, i.e., association data between WiFi users and access points, with an actual map of the space over which the traces were collected. Through a sequence of data processing steps, including filtering the data trace and converting the map to a graph representation, this framework generates a probabilistic mobility model that produces user movement patterns that are representative of real movement. This is done by adopting a set of heuristics that help us infer the paths users take between access points. We describe our experience applying this approach to a college campus, and study a number of properties of the trace data using our framework.
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...
Learning to Create DataIntegrating Queries
, 2008
"... The number of potentiallyrelated data resources available for querying — databases, data warehouses, virtual integrated schemas — continues to grow rapidly. Perhaps no area has seen this problem as acutely as the life sciences, where hundreds of large, complex, interlinked data resources are availa ..."
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Cited by 24 (9 self)
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The number of potentiallyrelated data resources available for querying — databases, data warehouses, virtual integrated schemas — continues to grow rapidly. Perhaps no area has seen this problem as acutely as the life sciences, where hundreds of large, complex, interlinked data resources are available on fields like proteomics, genomics, disease studies, and pharmacology. The schemas of individual databases are often large on their own, but users also need to pose queries across multiple sources, exploiting foreign keys and schema mappings. Since the users are not experts, they typically rely on the existence of predefined Web forms and associated query templates, developed by programmers to meet the particular scientists ’ needs. Unfortunately, such forms are scarce commodities, often limited to a single database, and mismatched with biologists’ information needs that are often contextsensitive and span multiple databases. We present a system with which a nonexpert user can author new query templates and Web forms, to be reused by anyone with related information needs. The user poses keyword queries that are matched against source relations and their attributes; the system uses sequences of associations (e.g., foreign keys, links, schema mappings, synonyms, and taxonomies) to create multiple ranked queries linking the matches to keywords; the set of queries is attached to a Web query form. Now the user and his or her associates may pose specific queries by filling in parameters in the form. Importantly, the answers to this query are ranked and annotated with data provenance, and the user provides feedback on the utility of the answers, from which the system ultimately learns to assign costs to sources and associations according to the user’s specific information need, as a result changing the ranking of the queries used to generate results. We evaluate the effectiveness of our method against “gold standard” costs from domain experts and demonstrate the method’s scalability.