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Using Difficulty of Prediction to Decrease Computation: Fast Sort, Priority Queue and Convex Hull on Entropy Bounded Inputs
"... There is an upsurge in interest in the Markov model and also more general stationary ergodic stochastic distributions in theoretical computer science community recently (e.g. see [Vitter,KrishnanSl], [Karlin,Philips,Raghavan92], [Raghavan9 for use of Markov models for online algorithms, e.g., cashi ..."
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Cited by 17 (4 self)
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There is an upsurge in interest in the Markov model and also more general stationary ergodic stochastic distributions in theoretical computer science community recently (e.g. see [Vitter,KrishnanSl], [Karlin,Philips,Raghavan92], [Raghavan9 for use of Markov models for online algorithms, e.g., cashing and prefetching). Their results used the fact that compressible sources are predictable (and vise versa), and showed that online algorithms can improve their performance by prediction. Actual page access sequences are in fact somewhat compressible, so their predictive methods can be of benefit. This paper investigates the interesting idea of decreasing computation by using learning in the opposite way, namely to determine the difficulty of prediction. That is, we will ap proximately learn the input distribution, and then improve the performance of the computation when the input is not too predictable, rather than the reverse. To our knowledge,
Efficient Lossless Compression of Trees and Graphs
 In IEEE Data Compression Conference (DCC
, 1996
"... In this paper, we study the problem of compressing a data structure (e.g. tree, undirected and directed graphs) in an efficient way while keeping a similar structure in the compressed form. To date, there has been no proven optimal algorithm for this problem. We use the idea of building LZW tree in ..."
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Cited by 6 (0 self)
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In this paper, we study the problem of compressing a data structure (e.g. tree, undirected and directed graphs) in an efficient way while keeping a similar structure in the compressed form. To date, there has been no proven optimal algorithm for this problem. We use the idea of building LZW tree in LZW compression to compress a binary tree generated by a stationary ergodic source in an optimal manner. We also extend our tree compression algorithm to compress undirected and directed acyclic graphs.
Using Learning and Difficulty of Prediction to Decrease Computation: A Fast Sort and Priority Queue on Entropy Bounded Inputs ∗
"... There is an upsurge in interest in the Markov model and also more general stationary ergodic stochastic distributions in theoretical computer science community recently, (e.g. see [Vitter,Krishnan,FOCS91], [Karlin,Philips,Raghavan,FOCS92] [Raghavan92]) for use of Markov models for online algorithms ..."
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There is an upsurge in interest in the Markov model and also more general stationary ergodic stochastic distributions in theoretical computer science community recently, (e.g. see [Vitter,Krishnan,FOCS91], [Karlin,Philips,Raghavan,FOCS92] [Raghavan92]) for use of Markov models for online algorithms e.g., cashing and prefetching). Their results used the fact that compressible sources are predictable (and vise versa), and show that online algorithms can improve their performance by prediction. Actual page access sequences are in fact somewhat compressible, so their predictive methods can be of benefit. This paper investigates the interesting idea of decreasing computation by using learning in the opposite way, namely to determine the difficulty of prediction. That is, we will approximately learn the input distribution, and then improve the performance of the computation when the input is not too predictable, rather than the reverse. To our knowledge, this is first case of a computational problem where we do not assume any particular fixed input distribution and yet computation is decreased when the input is less predictable, rather than the reverse. We concentrate our investigation on a basic computational problem: sorting and a basic data structure problem: maintaining a priority queue. We present the first known case of sorting and priority queue algorithms whose complexity depends on the binary entropy H ≤ 1 of input keys where assume that input keys are generated from an unknown but arbitrary stationary ergodic source. This is, we assume that each of the input keys can be each arbitrarily long, but have entropy H. Note that H
OffLine DictionaryBased Compression
"... Dictionarybased modeling is a mechanism used in many practical compression schemes. In most implementations of dictionarybased compression the encoder operates online, incrementally inferring its dictionary of available phrases from previous parts of the message. An alternative approach is to use ..."
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Dictionarybased modeling is a mechanism used in many practical compression schemes. In most implementations of dictionarybased compression the encoder operates online, incrementally inferring its dictionary of available phrases from previous parts of the message. An alternative approach is to use the full message to infer a complete dictionary in advance, and include an explicit representation of the dictionary as part of the compressed message. In this investigation, we develop a compression scheme that is a combination of a simple but powerful phrase derivation method and a compact dictionary encoding. The scheme is highly efficient, particularly in decompression, and has characteristics that make it a favorable choice when compressed data is to be searched directly. We describe data structures and algorithms that allow our mechanism to operate in linear time and space. Keywords—Dictionarybased modeling, hierarchical modeling, phrasebased compression, text compression. I.