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119
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...
Approximating the nondominated front using the Pareto Archived Evolution Strategy
 EVOLUTIONARY COMPUTATION
, 2000
"... We introduce a simple evolution scheme for multiobjective optimization problems, called the Pareto Archived Evolution Strategy (PAES). We argue that PAES may represent the simplest possible nontrivial algorithm capable of generating diverse solutions in the Pareto optimal set. The algorithm, in its ..."
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Cited by 236 (18 self)
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We introduce a simple evolution scheme for multiobjective optimization problems, called the Pareto Archived Evolution Strategy (PAES). We argue that PAES may represent the simplest possible nontrivial algorithm capable of generating diverse solutions in the Pareto optimal set. The algorithm, in its simplest form, is a (1 + 1) evolution strategy employing local search but using a reference archive of previously found solutions in order to identify the approximate dominance ranking of the current and candidate solution vectors. (1 + 1)PAES is intended to be a baseline approach against which more involved methods may be compared. It may also serve well in some realworld applications when local search seems superior to or competitive with populationbased methods. We introduce (1 + λ) and (μ  λ) variants of PAES as extensions to the basic algorithm. Six variants of PAES are compared to variants of the Niched Pareto Genetic Algorithm and the Nondominated Sorting Genetic Algorithm over a diverse suite of six test functions. Results are analyzed and presented using techniques that reduce the attainment surfaces generated from several optimization runs into a set of univariate distributions. This allows standard statistical analysis to be carried out for comparative purposes. Our results provide strong evidence that PAES performs consistently well on a range of multiobjective optimization tasks.
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...
Timing Driven Placement for Large Standard Cell Circuits
"... We present an algorithm for accurately controlling delays during the placement of large standard cell integrated circuits. Previous approaches to timing driven placement could not handle circuits containing 20,000 or more cells and yielded placement qualities which were well short of the state of th ..."
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Cited by 72 (1 self)
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We present an algorithm for accurately controlling delays during the placement of large standard cell integrated circuits. Previous approaches to timing driven placement could not handle circuits containing 20,000 or more cells and yielded placement qualities which were well short of the state of the art. Our timing optimization algorithm has been added to the placement algorithm which has yielded the best results ever reported on the full set of MCNC benchmark circuits, including a circuit containing more than 100,000 cells. A novel pinpair algorithm controls the delay without the need for user path specification. The timing algorithm is generally applicable to hierarchical, iterative placement methods. Using this algorithm, we present results for the only MCNC standard cell benchmark circuits (fract, struct, and avq.small) for which timing information is available. We decreased the delay of the longest path of circuit fract by 36 % at an area cost of only 2.5%. For circuit struct, the delay of the longest path was decreased by 50 % at an area cost of 6%. Finally, for the large (21,000 cell) circuit avq.small, the longest path delay was decreased by 28 % at an area cost of 6%.
An Iterative Algorithm for DelayConstrained MinimumCost Multicasting
 IEEE/ACM Transactions on Networking
, 1998
"... The bounded shortest multicast algorithm (BSMA) is presented for constructing minimumcost multicast trees with delay constraints. BSMA can handle asymmetric link characteristics and variable delay bounds on destinations, specified as real values, and minimizes the total cost of a multicast routing ..."
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Cited by 45 (1 self)
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The bounded shortest multicast algorithm (BSMA) is presented for constructing minimumcost multicast trees with delay constraints. BSMA can handle asymmetric link characteristics and variable delay bounds on destinations, specified as real values, and minimizes the total cost of a multicast routing tree. Instead of the singlepass tree construction approach used in most previous heuristics, the new algorithm is based on a feasiblesearch optimization strategy that starts with the minimumdelay multicast tree and monotonically decreases the cost by iterative improvement of the delaybounded multicast tree. BSMA's expected time complexity is analyzed, and simulation results are provided showing that BSMA can achieve nearoptimal cost reduction with fast execution.
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.
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.
Graph Kernels
, 2007
"... We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexit ..."
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Cited by 37 (4 self)
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We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexity of kernel computation between unlabeled graphs with n vertices from O(n 6) to O(n 3). We find a spectral decomposition approach even more efficient when computing entire kernel matrices. For labeled graphs we develop conjugate gradient and fixedpoint methods that take O(dn 3) time per iteration, where d is the size of the label set. By extending the necessary linear algebra to Reproducing Kernel Hilbert Spaces (RKHS) we obtain the same result for ddimensional edge kernels, and O(n 4) in the infinitedimensional case; on sparse graphs these algorithms only take O(n 2) time per iteration in all cases. Experiments on graphs from bioinformatics and other application domains show that these techniques can speed up computation of the kernel by an order of magnitude or more. We also show that certain rational kernels (Cortes et al., 2002, 2003, 2004) when specialized to graphs reduce to our random walk graph kernel. Finally, we relate our framework to Rconvolution kernels (Haussler, 1999) and provide a kernel that is close to the optimal assignment kernel of Fröhlich et al. (2006) yet provably positive semidefinite.
An energyaware QoS routing protocol for wireless sensor networks
 Proc. of the IEEE Workshop on Mobile and Wireless Networks (MWN 2003
, 2003
"... Recent advances in wireless sensor networks have led to many new routing protocols specifically designed for sensor networks. Almost all of these routing protocols considered energy efficiency as the ultimate objective in order to maximize the whole network lifetime. However, the introduction of vid ..."
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Cited by 37 (3 self)
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Recent advances in wireless sensor networks have led to many new routing protocols specifically designed for sensor networks. Almost all of these routing protocols considered energy efficiency as the ultimate objective in order to maximize the whole network lifetime. However, the introduction of video and imaging sensors has posed additional challenges. Transmission of video and imaging data requires both energy and QoS aware routing in order to ensure efficient usage of the sensors and effective access to the gathered measurements. In this paper, we propose an energyaware QoS routing protocol for sensor networks which can also run efficiently with besteffort traffic. The protocol finds a leastcost, delayconstrained path for realtime data in terms of link cost that captures nodes ’ energy reserve, transmission energy, error rate and other communication parameters. Moreover, the throughput for nonrealtime data is maximized by adjusting the service rate for both realtime and nonrealtime data at the sensor nodes. Simulation results have demonstrated the effectiveness of our approach for different metrics. 1.