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A New Algorithm for Building Alphabetic Minimax Trees
, 2008
"... We show how to build an alphabetic minimax tree for a sequence W = w1,...,wn of real weights in O(nd log log n) time, where d is the number of distinct integers ⌈wi⌉. We apply this algorithm to building an alphabetic prefix code given a sample. ..."
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Cited by 2 (2 self)
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We show how to build an alphabetic minimax tree for a sequence W = w1,...,wn of real weights in O(nd log log n) time, where d is the number of distinct integers ⌈wi⌉. We apply this algorithm to building an alphabetic prefix code given a sample.
Efficient Simplification of Bisimulation Formulas
 In Proceedings of the Workshop on Tools and Algorithms for the Construction and Analysis of Systems, pages 111132. LNCS 1019
, 1995
"... The problem of checking or optimally simplifying bisimulation formulas is likely to be computationally very hard. We take a different view at the problem: we set out to define a very fast algorithm, and then see what we can obtain. Sometimes our algorithm can simplify a formula perfectly, sometimes ..."
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Cited by 1 (0 self)
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The problem of checking or optimally simplifying bisimulation formulas is likely to be computationally very hard. We take a different view at the problem: we set out to define a very fast algorithm, and then see what we can obtain. Sometimes our algorithm can simplify a formula perfectly, sometimes it cannot. However, the algorithm is extremely fast and can, therefore, be added to formulabased bisimulation model checkers at practically no cost. When the formula can be simplified by our algorithm, this can have a dramatic positive effect on the better, but also more time consuming, theorem provers which will finish the job. 1 Introduction The need for validity checking or optimal simplification of first order bisimulation formulas has arisen from recent work on symbolic bisimulation checking of valuepassing calculi [4, 9, 15]. The NPcompleteness of checking satisfiability of propositional formulas [3] implies that validity checking of that class of formulas is coNP complete. Addit...
Retroactive data structures (extended abstract)
 IN SODA ’04: PROCEEDINGS OF THE FIFTEENTH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 2004
"... We introduce a new data structuring paradigm in which operations can be performed on a data structure not only in the present but also in the past. In this new paradigm, called retroactive data structures, the historical sequence of operations performed on the data structure is not fixed. The data s ..."
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We introduce a new data structuring paradigm in which operations can be performed on a data structure not only in the present but also in the past. In this new paradigm, called retroactive data structures, the historical sequence of operations performed on the data structure is not fixed. The data structure allows arbitrary insertion and deletion of operations at arbitrary times, subject only to consistency requirements. We initiate the study of retroactive data structures by formally defining the model and its variants. We prove that, unlike persistence, efficient retroactivity is not always achievable, so we go on to present several specific retroactive data structures.
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"... Abstract. We introduce a new data structuring paradigm in which operations can be performed on a data structure not only in the present but also in the past. In this new paradigm, called retroactive data structures, the historical sequence of operations performed on the data structure is not fixed. ..."
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Abstract. We introduce a new data structuring paradigm in which operations can be performed on a data structure not only in the present but also in the past. In this new paradigm, called retroactive data structures, the historical sequence of operations performed on the data structure is not fixed. The data structure allows arbitrary insertion and deletion of operations at arbitrary times, subject only to consistency requirements. We initiate the study of retroactive data structures by formally defining the model and its variants. We prove that, unlike persistence, efficient retroactivity is not always achievable. Thus, we present efficient retroactive data structures for queues, doubly ended queues, priority queues, unionfind, and decomposable search structures.
IOS Press A New Algorithm for Building Alphabetic Minimax Trees
"... Abstract. We show how to build an alphabetic minimax tree for a sequence W = w1,..., wn of real weights in O(nd log logn) time, where d is the number of distinct integers ⌈wi⌉. We apply this algorithm to building an alphabetic prefix code given a sample. ..."
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Abstract. We show how to build an alphabetic minimax tree for a sequence W = w1,..., wn of real weights in O(nd log logn) time, where d is the number of distinct integers ⌈wi⌉. We apply this algorithm to building an alphabetic prefix code given a sample.