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21
Shortest Path Algorithms: Engineering Aspects
 In Proc. ESAAC ’01, Lecture Notes in Computer Science
, 2001
"... We review shortest path algorithms based on the multilevel bucket data structure [6] and discuss the interplay between theory and engineering choices that leads to e#cient implementations. Our experimental results suggest that the caliber heuristic [17] and adaptive parameter selection give an ..."
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Cited by 20 (3 self)
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We review shortest path algorithms based on the multilevel bucket data structure [6] and discuss the interplay between theory and engineering choices that leads to e#cient implementations. Our experimental results suggest that the caliber heuristic [17] and adaptive parameter selection give an e#cient algorithm, both on typical and on hard inputs, for a wide range of arc lengths.
A New Evolutionary Approach to the Degree Constrained Minimum Spanning Tree Problem
 IEEE Transactions on Evolutionary Computation
, 2000
"... Finding the degreeconstrained minimum spanning tree (dMST) of a graph is a well studied NPhard problem which is important in network design. We introduce a new method which improves on the best technique previously published for solving the dMST, either using heuristic or evolutionary app ..."
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Cited by 11 (0 self)
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Finding the degreeconstrained minimum spanning tree (dMST) of a graph is a well studied NPhard problem which is important in network design. We introduce a new method which improves on the best technique previously published for solving the dMST, either using heuristic or evolutionary approaches. The basis of this encoding is a spanningtree construction algorithm which we call the Randomised Primal Method (RPM), based on the wellknown Prim's algorithm [6], and an extension [4] which we call `dPrim's'. We describe a novel encoding for spanning trees, which involves using the RPM to interpret lists of potential edges to include in the growing tree. We also describe a random graph generator which produces particularly challenging dMST problems. On these and other problems, we find that an evolutionary algorithm (EA) using the RPM encoding outperforms the previous best published technique from the operations research literature, and also outperforms simulated...
A Practical Minimum Spanning Tree Algorithm Using the Cycle Property
 IN 11TH EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA), NUMBER 2832 IN LNCS
, 2003
"... We present a simple new (randomized) algorithm for computing minimum spanning trees that is more than two times faster than the best previously known algorithms (for dense, "difficult" inputs). It is of conceptual interest that the algorithm uses the property that the heaviest edge in a cy ..."
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Cited by 11 (3 self)
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We present a simple new (randomized) algorithm for computing minimum spanning trees that is more than two times faster than the best previously known algorithms (for dense, "difficult" inputs). It is of conceptual interest that the algorithm uses the property that the heaviest edge in a cycle can be discarded. Previously this has only been exploited in asymptotically optimal algorithms that are considered impractical. An additional advantage is...
A New Evolutionary Approach to the DegreeConstrained Minimum Spanning Tree Problem
 IEEE Transactions on Evolutionary Computation
, 1999
"... Finding the degreeconstrained minimum spanning tree (dMST) of a graph is a wellstudied NPhard problem of importance in communications network design and other networkrelated problems. In this paper we describe some previously proposed algorithms for solving the problem, and then introduce a nove ..."
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Cited by 10 (2 self)
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Finding the degreeconstrained minimum spanning tree (dMST) of a graph is a wellstudied NPhard problem of importance in communications network design and other networkrelated problems. In this paper we describe some previously proposed algorithms for solving the problem, and then introduce a novel tree construction algorithm called the Randomised Primal Method (RPM) which builds degreeconstrained trees of low cost from solution vectors taken as input. RPM is applied in three stochastic iterative search methods: simulated annealing, multistart hillclimbing, and a genetic algorithm. While other researchers have mainly concentrated on finding spanning trees in Euclidean graphs, we consider the more general case of random graph problems. We describe two random graph generators which produce particularly challenging dMST problems. On these and other problems we find that the genetic algorithm employing RPM outperforms simulated annealing and multistart hillclimbing. Our experimental ...
RandomTree Diameter and the DiameterConstrained MST
 CONGRESSUS NUMERANTIUM
, 2000
"... A minimum spanning tree (MST) with a small diameter is required in numerous practical situations. It is needed, for example, in distributed mutual exclusion algorithms in order to minimize the number of messages communicated among processors per critical section. Understanding the behavior of tre ..."
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Cited by 10 (1 self)
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A minimum spanning tree (MST) with a small diameter is required in numerous practical situations. It is needed, for example, in distributed mutual exclusion algorithms in order to minimize the number of messages communicated among processors per critical section. Understanding the behavior of tree diameter is useful, for example, in determining an upper bound on the expected number of links between two arbitrary documents on the World Wide Web. The DiameterConstrained MST (DCMST) problem can be stated as follows: given an undirected, edgeweighted graph G with n nodes and a positive integer k, find a spanning tree with the smallest weight among all spanning trees of G which contain no path with more than k edges. This problem is known to be NPcomplete, for all values of k; 4 k #n  2). In this paper, we investigate the behavior of the diameter of MST in randomlyweighted complete graphs (in ErdősRnyi sense) and explore heuristics for the DCMST problem. For the case when the diameter bound k is smallindependent of n, we present a onetimetreeconstruction (OTTC) algorithm. It constructs a DCMST in a modified greedy fashion, employing a heuristic for selecting an edge to be added to the tree at each stage of the tree construction. This algorithm is fast and easily parallelizable. We also present a second algorithm that outperforms OTTC for larger values of k. It starts by generating an unconstrained MST and iteratively refines it by replacing edges, one by one, in the middle of long paths in the spanning tree until there is no path left with more than k edges. As expected, the performance of this heuristic is determined by the diameter of the unconstrained MST in the given graph. We discuss convergence, relative merits, and implementation of t...
Computing A DiameterConstrained Minimum Spanning Tree
, 2001
"... In numerous practical applications, it is necessary to find the smallest possible tree with a bounded diameter. A diameterconstrained minimum spanning tree (DCMST) of a given undirected, edgeweighted graph, G, is the smallestweight spanning tree of all spanning trees of G which contain no path wi ..."
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Cited by 8 (0 self)
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In numerous practical applications, it is necessary to find the smallest possible tree with a bounded diameter. A diameterconstrained minimum spanning tree (DCMST) of a given undirected, edgeweighted graph, G, is the smallestweight spanning tree of all spanning trees of G which contain no path with more than k edges, where k is a given positive integer. The problem of finding a DCMST is NPcomplete for all values of k; 4 k (n  2), except when all edgeweights are identical. A DCMST is essential for the efficiency of various distributed mutual exclusion algorithms, where it can minimize the number of messages communicated among processors per critical section. It is also useful in linear lightwave networks, where it can minimize interference in the network by limiting the traffic in the network lines. Another practical application requiring a DCMST arises in data compression, where some algorithms compress a file utilizing a tree datastructure, and decompress a path in the tree to access a record. A DCMST helps such algorithms to be fast without sacrificing a lot of storage space. We present a survey of the literature on the DCMST problem, study the expected diameter of a random labeled tree, and present five new polynomialtime algorithms for an approximate DCMST. One of our new algorithms constructs an approximate DCMST in a modified greedy fashion, employing a heuristic for selecting an edge to be added to iii the tree in each stage of the construction. Three other new algorithms start with an unconstrained minimum spanning tree, and iteratively refine it into an approximate DCMST. We also present an algorithm designed for the special case when the diameter is required to be no more than 4. Such a diameter4 tree is also used for evaluating the quality of o...
Optimal incremental sorting
 In Proc. 8th Workshop on Algorithm Engineering and Experiments (ALENEX
, 2006
"... Let A be a set of size m. Obtaining the first k ≤ m elements of A in ascending order can be done in optimal O(m+k log k) time. We present an algorithm (online on k) which incrementally gives the next smallest element of the set, so that the first k elements are obtained in optimal time for any k. We ..."
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Cited by 7 (5 self)
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Let A be a set of size m. Obtaining the first k ≤ m elements of A in ascending order can be done in optimal O(m+k log k) time. We present an algorithm (online on k) which incrementally gives the next smallest element of the set, so that the first k elements are obtained in optimal time for any k. We also give a practical algorithm with the same complexity on average, which improves in practice the existing online algorithm. As a direct application, we use our technique to implement Kruskal’s Minimum Spanning Tree algorithm, where our solution is competitive with the best current implementations. We finally show that our technique can be applied to several other problems, such as obtaining an interval of the sorted sequence and implementing heaps. 1
Mobile telemedicine sensor networks with lowenergy data query and network lifetime considerations
 IEEE Transactions on Mobile Computing
, 2006
"... Abstract—In this paper, we use an integrated architecture that takes advantage of the low cost mobile sensor networks and 3G cellular networks to accommodate multimedia medical calls with differentiated QualityofService (QoS) requirements. We propose a lowenergy, distributed, and concentriczoneb ..."
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Cited by 7 (4 self)
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Abstract—In this paper, we use an integrated architecture that takes advantage of the low cost mobile sensor networks and 3G cellular networks to accommodate multimedia medical calls with differentiated QualityofService (QoS) requirements. We propose a lowenergy, distributed, and concentriczonebased data query mechanism that takes advantages of hierarchical ad hoc routing algorithms to enable a medical specialist to collect physiological data from mobile and/or remote patients. The medical specialist uses cellular network to report patients ’ data to the medical center. Moreover, we propose a transmission scheme among different zones with balancebased energy efficiency, which can extend network lifetime. We evaluate the validity of our proposals through simulations and analyze their performance. Our results clearly indicate the energy efficiency of the proposed sensor network query algorithms and the efficiency of our multiclass medical call admission control scheme in terms of meeting the multimedia telemedicine QoS requirements. Index Terms — Mobile telemedicine, ad hoc networks, sensor networks, 3G wireless cellular networks. æ 1
A Practical Shortest Path Algorithm with Linear Expected Time
 SUBMITTED TO SIAM J. ON COMPUTING
, 2001
"... We present an improvement of the multilevel bucket shortest path algorithm of Denardo and Fox [9] and justify this improvement, both theoretically and experimentally. We prove that if the input arc lengths come from a natural probability distribution, the new algorithm runs in linear average time ..."
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Cited by 4 (1 self)
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We present an improvement of the multilevel bucket shortest path algorithm of Denardo and Fox [9] and justify this improvement, both theoretically and experimentally. We prove that if the input arc lengths come from a natural probability distribution, the new algorithm runs in linear average time while the original algorithm does not. We also describe an implementation of the new algorithm. Our experimental data suggests that the new algorithm is preferable to the original one in practice. Furthermore, for integral arc lengths that fit into a word of today's computers, the performance is close to that of breadthfirst search, suggesting limitations on further practical improvements.