Results 11  20
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35
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
Minimizing Randomness in Minimum Spanning Tree, Parallel Connectivity, and Set Maxima Algorithms
 In Proc. 13th Annual ACMSIAM Symposium on Discrete Algorithms (SODA'02
, 2001
"... There are several fundamental problems whose deterministic complexity remains unresolved, but for which there exist randomized algorithms whose complexity is equal to known lower bounds. Among such problems are the minimum spanning tree problem, the set maxima problem, the problem of computing conne ..."
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Cited by 7 (4 self)
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There are several fundamental problems whose deterministic complexity remains unresolved, but for which there exist randomized algorithms whose complexity is equal to known lower bounds. Among such problems are the minimum spanning tree problem, the set maxima problem, the problem of computing connected components and (minimum) spanning trees in parallel, and the problem of performing sensitivity analysis on shortest path trees and minimum spanning trees. However, while each of these problems has a randomized algorithm whose performance meets a known lower bound, all of these randomized algorithms use a number of random bits which is linear in the number of operations they perform. We address the issue of reducing the number of random bits used in these randomized algorithms. For each of the problems listed above, we present randomized algorithms that have optimal performance but use only a polylogarithmic number of random bits; for some of the problems our optimal algorithms use only log n random bits. Our results represent an exponential savings in the amount of randomness used to achieve the same optimal performance as in the earlier algorithms. Our techniques are general and could likely be applied to other problems.
On the ComparisonAddition Complexity of AllPairs Shortest Paths
 In Proc. 13th Int'l Symp. on Algorithms and Computation (ISAAC'02
, 2002
"... We present an allpairs shortest path algorithm for arbitrary graphs that performs O(mn log (m; n)) comparison and addition operations, where m and n are the number of edges and vertices, resp., and is Tarjan's inverseAckermann function. Our algorithm eliminates the sorting bottleneck inherent in a ..."
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Cited by 6 (5 self)
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We present an allpairs shortest path algorithm for arbitrary graphs that performs O(mn log (m; n)) comparison and addition operations, where m and n are the number of edges and vertices, resp., and is Tarjan's inverseAckermann function. Our algorithm eliminates the sorting bottleneck inherent in approaches based on Dijkstra's algorithm, and for graphs with O(n) edges our algorithm is within a tiny O(log (n; n)) factor of optimal. Our algorithm can be implemented to run in polynomial time (granted, a large polynomial). We leave open the problem of providing an efficient implementation.
CTL Model Update for System Modifications
"... Model checking is a promising technology, which has been applied for verification of many hardware and software systems. In this paper, we introduce the concept of model update towards the development of an automatic system modification tool that extends model checking functions. We define primitive ..."
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Cited by 4 (0 self)
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Model checking is a promising technology, which has been applied for verification of many hardware and software systems. In this paper, we introduce the concept of model update towards the development of an automatic system modification tool that extends model checking functions. We define primitive update operations on the models of Computation Tree Logic (CTL) and formalize the principle of minimal change for CTL model update. These primitive update operations, together with the underlying minimal change principle, serve as the foundation for CTL model update. Essential semantic and computational characterizations are provided for our CTL model update approach. We then describe a formal algorithm that implements this approach. We also illustrate two case studies of CTL model updates for the wellknown microwave oven example and the Andrew File System 1, from which we further propose a method to optimize the update results in complex system modifications. 1.
Efficient Algorithms for Single Link Failure Recovery and Its Application To Atm Networks
 In Proc. 15th IASTED Intl. Conf. on PDCS
, 2003
"... We investigate the single link failure recovery problem and its application to the alternate path routing problem for ATM networks. Specifically, given a 2connected graph G, a specified node s, and a shortest paths tree T s = fe 1 ; e 2 ; : : : ; e n\Gamma1 g of s, where e i = (x i ; y i ) and x i ..."
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Cited by 4 (3 self)
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We investigate the single link failure recovery problem and its application to the alternate path routing problem for ATM networks. Specifically, given a 2connected graph G, a specified node s, and a shortest paths tree T s = fe 1 ; e 2 ; : : : ; e n\Gamma1 g of s, where e i = (x i ; y i ) and x i = parent Ts (y i ), find a shortest path from y i to s in the graph Gne i for 1 i n \Gamma 1. We present an O(m + n log n) time algorithm for this problem and a linear time algorithm for the case when all weights are equal. When the edge weights are integers, we present an algorithm that takes O(m+ T sort (n)) time where T sort (n) is the time required to sort n integers. We show that any solution to the single link recovery problem can adapted to solve the alternate path routing problem in ATM networks.
Two Linear Time Algorithms for MST on Minor Closed Graph Classes
, 2002
"... This article presents two simple deterministic algorithms for finding the Minimum Spanning Tree in O(V + E) time for any proper class of graphs closed on graph minors, which includes planar graphs and graphs of bounded genus. Both algorithms require no a priori knowledge of the structure of th ..."
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Cited by 3 (0 self)
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This article presents two simple deterministic algorithms for finding the Minimum Spanning Tree in O(V + E) time for any proper class of graphs closed on graph minors, which includes planar graphs and graphs of bounded genus. Both algorithms require no a priori knowledge of the structure of the class except for its density; edge weights are only compared and no random access to data is needed.
An InverseAckermann Style Lower Bound for Online Minimum Spanning Tree Verification
 Combinatorica
"... 1 Introduction The minimum spanning tree (MST) problem has seen a flurry of activity lately, driven largely by the success of a new approach to the problem. The recent MST algorithms [20, 8, 29, 28], despite their superficial differences, are all based on the idea of progressively improving an appro ..."
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Cited by 3 (2 self)
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1 Introduction The minimum spanning tree (MST) problem has seen a flurry of activity lately, driven largely by the success of a new approach to the problem. The recent MST algorithms [20, 8, 29, 28], despite their superficial differences, are all based on the idea of progressively improving an approximately minimum solution, until the actual minimum spanning tree is found. It is still likely that this progressive improvement approach will bear fruit. However, the current
On an Online Spanning Tree Problem in Randomly Weighted Graphs
 Combinatorics, Probability and Computing
, 2005
"... This paper is devoted to an online variant of the minimum spanning tree problem in randomly weighted graphs. We assume that the input graph is complete and the edge weights are uniform distributed over [0, 1]. An algorithm receives the edges one by one and has to decide immediately whether to includ ..."
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Cited by 3 (1 self)
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This paper is devoted to an online variant of the minimum spanning tree problem in randomly weighted graphs. We assume that the input graph is complete and the edge weights are uniform distributed over [0, 1]. An algorithm receives the edges one by one and has to decide immediately whether to include the current edge into the spanning tree or to reject it. The corresponding edge sequence is determined by some adversary. We propose an algorithm which achieves E [ALG] /E [OPT] = O (1) and E [ALG/OPT] = O (1) against a fair adaptive adversary, i.e., an adversary which determines the edge order online and is fair in a sense that he does not know more about the edge weights than the algorithm. Furthermore, we prove that no online algorithm performs better than E [ALG] /E [OPT] =# (log n) if the adversary knows the edge weights in advance. This lower bound is tight, since there is an algorithm which yields E [ALG] /E [OPT] = O (log n) against the strongest imaginable adversary. 1.
Modeling of physical carrier sense in multihop wireless networks and its use in joint power control and carrier sense adjustment
, 2006
"... Abstract — In this paper, we extend both Bianchi’s and Kumar’s models and characterize the channel activities governed by IEEE 802.11 DCF in multihop wireless networks from the perspective of an individual sender. In particular, we incorporate the effect of PHY/MAC attributes (such as transmit powe ..."
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Cited by 2 (2 self)
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Abstract — In this paper, we extend both Bianchi’s and Kumar’s models and characterize the channel activities governed by IEEE 802.11 DCF in multihop wireless networks from the perspective of an individual sender. In particular, we incorporate the effect of PHY/MAC attributes (such as transmit power and physical carrier sense) that need not be considered in WLANs but become extraordinarily important in multihop wireless networks, and derive the throughput attained by each sender. With the use of the analytical model derived, we investigate the impact of transmit power and carrier sense threshold on network capacity, and identify a simple operating condition under which the network may attain throughput that is close to its optimal value. Based on the insight shed from the analytical model, we then propose a distributed and localized algorithm, called Local Minimum Spanning Tree with Carrier Sense Adjustment (LMSTCSA) that determines both the transmit power and the carrier sense threshold of a node. We evaluate LMSTCSA via JSim simulation [1]. Simulation results show that LMSTCSA achieves higher throughput as compared to conventional IEEE 802.11 DCF, LMST with no carrier sense adjustment, and LMST with static carrier sense adjustment. I.
A Simpler Implementation and Analysis of Chazelle’s Soft Heaps
 In Proc. of the 19th ACMSIAM Symposium on Discrete Algorithms
, 2009
"... Chazelle (JACM 47(6), 2000) devised an approximate meldable priority queue data structure, called Soft Heaps, and used it to obtain the fastest known deterministic comparisonbased algorithm for computing minimum spanning trees, as well as some new algorithms for selection and approximate sorting pr ..."
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Cited by 2 (0 self)
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Chazelle (JACM 47(6), 2000) devised an approximate meldable priority queue data structure, called Soft Heaps, and used it to obtain the fastest known deterministic comparisonbased algorithm for computing minimum spanning trees, as well as some new algorithms for selection and approximate sorting problems. If n elements are inserted into a collection of soft heaps, then up to εn of the elements still contained in these heaps, for a given error parameter ε, maybecorrupted, i.e., have their keys artificially increased. In exchange for allowing these corruptions, each soft heap operation is performed in O(log 1 ε) amortized time. Chazelle’s soft heaps are derived from the binomial heaps data structure in which each priority queue is composed of a collection of binomial trees. We describe a simpler and more direct implementation of soft heaps in which each priority queue is composed of a collection of standard binary trees. Our implementation has the advantage that no cleanup operations similar to the ones used in Chazelle’s implementation are required. We also present a concise and unified potentialbased amortized analysis of the new implementation. 1