Results 1  10
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25
A general approximation technique for constrained forest problems
 SIAM J. COMPUT.
, 1995
"... We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization proble ..."
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Cited by 423 (21 self)
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We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization problems fit in this framework, including the shortest path, minimumcost spanning tree, minimumweight perfect matching, traveling salesman, and Steiner tree problems. Our technique produces approximation algorithms that run in O(n log n) time and come within a factor of 2 of optimal for most of these problems. For instance, we obtain a 2approximation algorithm for the minimumweight perfect matching problem under the triangle inequality. Our running time of O(n log n) time compares favorably with the best strongly polynomial exact algorithms running in O(n 3) time for dense graphs. A similar result is obtained for the 2matching problem and its variants. We also derive the first approximation algorithms for many NPcomplete problems, including the nonfixed pointtopoint connection problem, the exact path partitioning problem, and complex locationdesign problems. Moreover, for the prizecollecting traveling salesman or Steiner tree problems, we obtain 2approximation algorithms, therefore improving the previously bestknown performance guarantees of 2.5 and 3, respectively [Math. Programming, 59 (1993), pp. 413420].
THE PRIMALDUAL METHOD FOR APPROXIMATION ALGORITHMS AND ITS APPLICATION TO NETWORK DESIGN PROBLEMS
"... The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent researc ..."
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Cited by 143 (5 self)
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The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent research applying the primaldual method to problems in network design.
Reach for A∗: Efficient pointtopoint shortest path algorithms
 IN WORKSHOP ON ALGORITHM ENGINEERING & EXPERIMENTS
, 2006
"... We study the pointtopoint shortest path problem in a setting where preprocessing is allowed. We improve the reachbased approach of Gutman [16] in several ways. In particular, we introduce a bidirectional version of the algorithm that uses implicit lower bounds and we add shortcut arcs which reduc ..."
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Cited by 76 (6 self)
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We study the pointtopoint shortest path problem in a setting where preprocessing is allowed. We improve the reachbased approach of Gutman [16] in several ways. In particular, we introduce a bidirectional version of the algorithm that uses implicit lower bounds and we add shortcut arcs which reduce vertex reaches. Our modifications greatly reduce both preprocessing and query times. The resulting algorithm is as fast as the best previous method, due to Sanders and Schultes [27]. However, our algorithm is simpler and combines in a natural way with A∗ search, which yields significantly better query times.
Computing PointtoPoint Shortest Paths from External Memory
"... We study the ALT algorithm [19] for the pointtopoint shortest path problem in the context of road networks. We suggest improvements to the algorithm itself and to its preprocessing stage. We also develop a memoryefficient implementation of the algorithm that runs on a Pocket PC. It stores graph d ..."
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Cited by 56 (6 self)
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We study the ALT algorithm [19] for the pointtopoint shortest path problem in the context of road networks. We suggest improvements to the algorithm itself and to its preprocessing stage. We also develop a memoryefficient implementation of the algorithm that runs on a Pocket PC. It stores graph data in a flash memory card and uses RAM to store information only for the part of the graph visited by the current shortest path computation. The implementation works even on very large graphs, including that of the North America road network, with almost 30 million vertices.
An Auction Algorithm for Shortest Paths
, 1991
"... We propose a new and simple algorithm for finding shortest paths in a directed graph. In the single origin/single destination case, the algorithm maintains a single path starting at the origin, which is extended or contracted by a single node at each iteration. Simultaneously, at most one dual varia ..."
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Cited by 29 (7 self)
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We propose a new and simple algorithm for finding shortest paths in a directed graph. In the single origin/single destination case, the algorithm maintains a single path starting at the origin, which is extended or contracted by a single node at each iteration. Simultaneously, at most one dual variable is adjusted at each iteration so as to either improve or maintain the value of a dual function. For the case of multiple origins, the algorithm is well suited for parallel computation. It maintains multiple paths that can be extended or contracted in parallel by several processors that share the results of their computations. Based on experiments with randomly generated problems on a serial machine, the algorithm outperforms substantially its closest competitors for problems with few origins and a single destination. It also seems better suited for parallel computation than other shortest path algorithms.
Monitoring path nearest neighbor in road networks
 In SIGMOD
, 2009
"... This paper addresses the problem of monitoring the k nearest neighbors to a dynamically changing path in road networks. Given a destination where a user is going to, this new query returns the kNN with respect to the shortest path connecting the destination and the user’s current location, and thus ..."
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Cited by 25 (3 self)
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This paper addresses the problem of monitoring the k nearest neighbors to a dynamically changing path in road networks. Given a destination where a user is going to, this new query returns the kNN with respect to the shortest path connecting the destination and the user’s current location, and thus provides a list of nearest candidates for reference by considering the whole coming journey. We name this query the kPath Nearest Neighbor query (kPNN). As the user is moving and may not always follow the shortest path, the query path keeps changing. The challenge of monitoring the kPNN for an arbitrarily moving user is to dynamically determine the update locations and then refresh the kPNN efficiently. We propose a threephase Bestfirst Network Expansion (BNE) algorithm for monitoring the kPNN and the corresponding shortest path. In the searching phase, the BNE finds the shortest path to the destination, during which a candidate set that guarantees to include the kPNN is generated at the same time. Then in the verification phase, a heuristic algorithm runs for examining candidates’ exact distances to the query path, and it achieves significant reduction in the number of visited nodes. The monitoring phase deals with computing update locations as well as refreshing the kPNN in different user movements. Since determining the network distance is a costly process, an expansion tree and the candidate set are carefully maintained by the BNE algorithm, which can provide efficient update on the shortest path and the kPNN results. Finally, we conduct extensive experiments on real road networks and show that our methods achieve satisfactory performance.
On kskip Shortest Paths
"... Given two vertices s, t in a graph, let P be the shortest path (SP) from s to t, and P ⋆ a subset of the vertices in P. P ⋆ is a kskip shortest path from s to t, if it includes at least a vertex out of every k consecutive vertices in P. In general, P ⋆ succinctly describes P by sampling the vertice ..."
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Cited by 9 (0 self)
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Given two vertices s, t in a graph, let P be the shortest path (SP) from s to t, and P ⋆ a subset of the vertices in P. P ⋆ is a kskip shortest path from s to t, if it includes at least a vertex out of every k consecutive vertices in P. In general, P ⋆ succinctly describes P by sampling the vertices in P with a rate of at least 1/k. This makes P ⋆ a natural substitute in scenarios where reporting every single vertex of P is unnecessary or even undesired. This paper studies kskip SP computation in the context of spatial network databases (SNDB). Our technique has two properties crucial for realtime query processing in SNDB. First, our solution is able to answer kskip queries significantly faster than finding the original SPs in their entirety. Second, the previous objective is achieved with a structure that occupies less space than storing the underlying road network. The proposed algorithms are the outcome of a careful theoretical analysis that reveals valuable insight into the characteristics of the kskip SP problem. Their efficiency has been confirmed by extensive experiments with real data.
Common Misconceptions Concerning Heuristic Search
"... This paper examines the following statements about heuristic search, which are commonly held to be true: More accurate heuristics result in fewer states being expanded by A * and IDA*. A * expands fewer states than any other equally informed algorithm that finds optimal solutions. Any admissible heu ..."
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Cited by 9 (2 self)
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This paper examines the following statements about heuristic search, which are commonly held to be true: More accurate heuristics result in fewer states being expanded by A * and IDA*. A * expands fewer states than any other equally informed algorithm that finds optimal solutions. Any admissible heuristic can be turned into a consistent heuristic by a simple technique called. In search spaces whose operators all have the same cost A * with the heuristic function for all states, , is the same as breadthfirst search. Bidirectional A * stops when the forward and backward search frontiers meet. The paper demonstrates that all these statements are false and provides alternative statements that are true.
A Cutting Plane Algorithm for the OneDimensional Cutting Stock Problem with Multiple Stock Lengths
 European Journal of Operational Research
, 2002
"... . A cutting plane approach combining ChvatalGomory cutting planes with column generation is generalized for the case of multiple stock lengths in the onedimensional cutting stock problem. Appropriate modications of the column generation procedure and the rounding heuristic are proposed. A comparis ..."
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Cited by 8 (5 self)
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. A cutting plane approach combining ChvatalGomory cutting planes with column generation is generalized for the case of multiple stock lengths in the onedimensional cutting stock problem. Appropriate modications of the column generation procedure and the rounding heuristic are proposed. A comparison with the branchandprice method for the problem with one stock type and representative test results are reported. Keywords: cutting, cutting planes, column generation, heuristics, branchandbound 1
PointtoPoint Shortest Path Algorithms with Preprocessing
"... This is a survey of some recent results on pointtopoint shortest path algorithms. This classical optimization problem received a lot of attention lately and significant progress has been made. After an overview of classical results, we study recent heuristics that solve the problem while examinin ..."
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Cited by 7 (0 self)
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This is a survey of some recent results on pointtopoint shortest path algorithms. This classical optimization problem received a lot of attention lately and significant progress has been made. After an overview of classical results, we study recent heuristics that solve the problem while examining only a small portion of the input graph; the graph can be very big. Note that the algorithms we discuss find exact shortest paths. These algorithms are heuristic because they perform well only on some graph classes. While their performance has been good in experimental studies, no theoretical bounds are known to support the experimental observations. Most of these algorithms have been motivated by finding paths in large road networks. We start by reviewing the classical Dijkstra’s algorithm and its bidirectional variant, developed in 1950’s and 1960’s. Then we review A* search, an AI technique developed in 1970’s. Next we turn our attention to modern results which are based on preprocessing the graph. To be practical, preprocessing needs to be reasonably fast and not use too much space. We discuss landmark and reachbased algorithms as well as their combination.