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31
Priority Queues and Dijkstra’s Algorithm
, 2007
"... We study the impact of using different priority queues in the performance of Dijkstra’s SSSP algorithm. We consider only general priority queues that can handle any type of keys (integer, floating point, etc.); the only exception is that we use as a benchmark the DIMACS Challenge SSSP code [1] which ..."
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We study the impact of using different priority queues in the performance of Dijkstra’s SSSP algorithm. We consider only general priority queues that can handle any type of keys (integer, floating point, etc.); the only exception is that we use as a benchmark the DIMACS Challenge SSSP code [1] which can handle only integer values for distances. Our experiments were focussed on the following: 1. We study the performance of two variants of Dijkstra’s algorithm: the wellknown version that uses a priority queue that supports the DecreaseKey operation, and another that uses a basic priority queue that supports only Insert and DeleteMin. For the latter type of priority queue we include several for which highperformance code is available such as bottomup binary heap, aligned 4ary heap, and sequence heap [33]. 2. We study the performance of Dijkstra’s algorithm designed for flat memory relative to versions that try to be cacheefficient. For this, in main part, we study the difference in performance of Dijkstra’s algorithm relative to the cacheefficiency of the priority queue used, both incore and outofcore. We also study the performance of an implementation
Discrete Event Systems in Rewriting Logic
, 1996
"... In this note, we report on some work in progress on using rewriting logics for discrete event simulation. The idea is to combine the proofs in the logic with the observations in the simulations to gain a better understanding of the interaction intricacies that seem to occur in complex simulations. I ..."
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In this note, we report on some work in progress on using rewriting logics for discrete event simulation. The idea is to combine the proofs in the logic with the observations in the simulations to gain a better understanding of the interaction intricacies that seem to occur in complex simulations. In particular, we use communication protocols as our application domain, since they have all the interaction and unpredictability that makes formal specifications difficult. 1 Problem: Formal Methods in Simulation The historical barriers to the use of formal methods in designing and developing communication protocols derive from their different attitudes: verification models have been used for many years for proofs of behavior (a verification model cannot tell you when the model is wrong), but simulation models are used for observations of behavior (a simulation model cannot tell you when the model is right). These are almost always different models, since they must concentrate on different ...
Pairing Heaps are Suboptimal
, 1997
"... Pairing heaps were introduced as a selfadjusting alternative to Fibonacci heaps. They provably enjoy log n amortized costs for the standard heap operations. Although it has not been verified that pairing heaps perform the decrease key operation in constant amortized time, this has been conjectured ..."
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Pairing heaps were introduced as a selfadjusting alternative to Fibonacci heaps. They provably enjoy log n amortized costs for the standard heap operations. Although it has not been verified that pairing heaps perform the decrease key operation in constant amortized time, this has been conjectured and extensive experimental evidence supports this conjecture. Moreover, pairing heaps have been observed to be superior to Fibonacci heaps in practice. However, as demonstrated in this paper, pairing heaps do not accommodate decrease key operations in constant amortized time. 1 Introduction Pairing heaps were introduced [1] as a selfadjusting alternative to Fibonacci heaps [2]. They are easy to code and provably enjoy log n amortized costs for the standard heap operations. Although it had not been verified that pairing heaps perform the decrease key operation in constant amortized time (the raison d'etre of Fibonacci heaps), this has been conjectured [1] and extensive experimental eviden...
RankRelaxed Weak Queues: Faster than Pairing and Fibonacci Heaps?
, 2009
"... A runrelaxed weak queue by Elmasry et al. (2005) is a priority queue data structure with insert and decreasekey in O(1) as well as delete and deletemin in O(log n) worstcase time. One further advantage is the small space consumption of 3n + O(log n) pointers. In this paper we propose rankrelaxe ..."
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A runrelaxed weak queue by Elmasry et al. (2005) is a priority queue data structure with insert and decreasekey in O(1) as well as delete and deletemin in O(log n) worstcase time. One further advantage is the small space consumption of 3n + O(log n) pointers. In this paper we propose rankrelaxed weak queues, reducing the number of rank violations nodes for each level to a constant, while providing amortized constant time for decreasekey. Compared to runrelaxed weak queues, the new structure additionally gains one pointer per node. An empirical evaluation shows that the implementation can outperform Fibonacci and pairing heaps in practice even on rather simple data types.
RankPairing Heaps
"... Abstract. We introduce the rankpairing heap, a heap (priority queue) implementation that combines the asymptotic efficiency of Fibonacci heaps with much of the simplicity of pairing heaps. Unlike all other heap implementations that match the bounds of Fibonacci heaps, our structure needs only one c ..."
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Abstract. We introduce the rankpairing heap, a heap (priority queue) implementation that combines the asymptotic efficiency of Fibonacci heaps with much of the simplicity of pairing heaps. Unlike all other heap implementations that match the bounds of Fibonacci heaps, our structure needs only one cut and no other structural changes per key decrease; the trees representing the heap can evolve to have arbitrary structure. Our initial experiments indicate that rankpairing heaps perform almost as well as pairing heaps on typical input sequences and better on worstcase sequences. 1
Pairing Heaps with Costless Meld
, 2009
"... Improving the structure and analysis in [1], we give a variation of the pairing heaps that has amortized zero cost per meld (compared to an O(log log n) in [1]) and the same amortized bounds for all other operations. More precisely, the new pairing heap requires: no cost per meld, O(1) per findmin ..."
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Improving the structure and analysis in [1], we give a variation of the pairing heaps that has amortized zero cost per meld (compared to an O(log log n) in [1]) and the same amortized bounds for all other operations. More precisely, the new pairing heap requires: no cost per meld, O(1) per findmin and insert, O(log n) per deletemin, and O(log log n) per decreasekey. These bounds are the best known for any selfadjusting heap, and match the lower bound proven by Fredman for a family of such heaps. Moreover, our structure is even simpler than that in [1].
© World Scientific Publishing Company TREE COMPRESSION AND OPTIMIZATION WITH APPLICATIONS Dedicated to the memory of Markku Tamminen (19451989)
, 1990
"... Different methods for compressing trees are surveyed and developed. Tree compression can be seen as a tradeoff problem between time and space in which we can choose different strategies depending on whether we prefer better compression results or more efficient operations in the compressed structur ..."
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Different methods for compressing trees are surveyed and developed. Tree compression can be seen as a tradeoff problem between time and space in which we can choose different strategies depending on whether we prefer better compression results or more efficient operations in the compressed structure. Of special interest is the case where space can be saved while preserving the functionality of the operations; this is called data optimization. The general compression scheme employed here consists of separate linearization of the tree structure and the data stored in the tree. Also some applications of the tree compression methods are explored. These include the syntaxdirected compression of program files, the compression of pixel trees, trie compaction and dictionaries maintained as implicit data structures.
By
, 2005
"... The growing awareness of the network vulnerability draws much attention to security from both the academic community and industrial society. Security is no longer a luxury but an independent and indispensable service to the current Internet. While various security mechanisms such as cryptographic an ..."
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The growing awareness of the network vulnerability draws much attention to security from both the academic community and industrial society. Security is no longer a luxury but an independent and indispensable service to the current Internet. While various security mechanisms such as cryptographic and intrusion detection techniques have been proposed, designed, and even deployed in the field, the newly exposed network vulnerabilities and the emerging network technologies create new security challenges which make the existing security solutions either inefficient or insufficient. My Ph D research focuses on the efficient protection on link state routing and the selforganizing and selfdependent hierarchical public key certificate management in the emerging mobile ad hoc networks. The contributions of this thesis include two parts. In the first part, a cost reduced secure link state routing protocol with the capability of detecting disruptive links is proposed to efficiently protect the routing control messages (e.g., LSA) and trace the faulty intermediate routers; then a confidence extended routing mechanism enhanced with secure virtual links is designed to increase network reachability through selectively including the uncertain routers in packet relaying and further continuously
A New Priority Queue for Simulation of Many Objects
"... During the discrete event simulation of complex systems based on many active/passive objects, the efficiency of the algorithm and data structure used to manage the events of the process is crucial. Both runtime and space used are relevant for the study of large systems. A main issue in the simulatio ..."
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During the discrete event simulation of complex systems based on many active/passive objects, the efficiency of the algorithm and data structure used to manage the events of the process is crucial. Both runtime and space used are relevant for the study of large systems. A main issue in the simulation of these systems are the interactions between pairs of objects. These interactions are treated as events that take place at discrete instants. The event management is performed by using a priority queue in which sequences of events are inserted/deleted in an efficient manner. In this paper we introduce and analyze a new priority queue  called Local Minima  which resembles a hybrid structure between the classical heap and linked lists. We also present empirical results showing that our priority queue is more efficient and stable than other alternatives in the simulation of molecular fluids. Systems with many moving objects  such as molecular fluids  are an important class of applica...