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Checking Geometric Programs or Verification of Geometric Structures
 IN PROC. 12TH ANNU. ACM SYMPOS. COMPUT. GEOM
, 1996
"... A program checker verifies that a particular program execution is correct. We give simple and efficient program checkers for some basic geometric tasks. We report about our experiences with program checking in the context of the LEDA system. We discuss program checking for data structures that ha ..."
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Cited by 30 (6 self)
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A program checker verifies that a particular program execution is correct. We give simple and efficient program checkers for some basic geometric tasks. We report about our experiences with program checking in the context of the LEDA system. We discuss program checking for data structures that have to rely on userprovided functions.
A Basis for Implementing Exact Geometric Algorithms (Extended Abstract)
, 1993
"... Our ultimate goal is to develop exact geometric computation as an viable alternative to the usual computing paradigm based on fixedprecision arithmetic. Use of exact computation has numerous advantages; in particular, it will abolish the nonrobustness issues that has so far defied satisfactory so ..."
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Cited by 15 (7 self)
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Our ultimate goal is to develop exact geometric computation as an viable alternative to the usual computing paradigm based on fixedprecision arithmetic. Use of exact computation has numerous advantages; in particular, it will abolish the nonrobustness issues that has so far defied satisfactory solution. In this paper we describe two computational tools which can be a basis for exact geometric computing: ffl bigFloat: a multiprecision floatingpoint number system with automatic errorhandling. ffl bigExpression: an expressions package based on a precisiondriven mechanism. This package is built on top of bigFloat. We discuss the rationale for the design of these packages. Experimental results are reported. The major contributions of our work are: ffl We demonstrated for the first time that, because of the existence of root...
Biased Skip Lists
 Algorithmica
, 2004
"... We design a variation of skip lists that performs well for generally biased access sequences. ..."
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Cited by 12 (1 self)
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We design a variation of skip lists that performs well for generally biased access sequences.
Adaptive Software: Automatic Navigation Through Partially Specified Data Structures
, 1994
"... ..."
Dynamic Optimality for Skip Lists and BTrees
, 2008
"... Sleator and Tarjan [39] conjectured that splay trees are dynamically optimal binary search trees (BST). In this context, we study the skip list data structure introduced by Pugh [35]. We prove that for a class of skip lists that satisfy a weak balancing property, the workingset bound is a lower bou ..."
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Cited by 5 (1 self)
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Sleator and Tarjan [39] conjectured that splay trees are dynamically optimal binary search trees (BST). In this context, we study the skip list data structure introduced by Pugh [35]. We prove that for a class of skip lists that satisfy a weak balancing property, the workingset bound is a lower bound on the time to access any sequence. Furthermore, we develop a deterministic selfadjusting skip list whose running time matches the workingset bound, thereby achieving dynamic optimality in this class. Finally, we highlight the implications our bounds for skip lists have on multiway branching search trees such as Btrees, (ab)trees, and other variants as well as their binary tree representations. In particular, we show a selfadjusting Btree that is dynamically optimal both in internal and external memory.
Efficient Strategies for Topics in Internet Algorithmics
, 2002
"... In this dissertation we posit a coherent area of research called Internet Algorithmics. We study a number of different algorithmic problems which are motivated by or are relevant to the various processes which activate the Internet or are activated by it. The first ..."
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Cited by 2 (0 self)
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In this dissertation we posit a coherent area of research called Internet Algorithmics. We study a number of different algorithmic problems which are motivated by or are relevant to the various processes which activate the Internet or are activated by it. The first
Selfadjusting Data Structures for External Memory String Access
, 2001
"... Data warehouses are increasingly storing and managing large scale string data, and dealing with large volume of transactions that update and search string databases. Motivated by this context, we initiate the study of selfadjusting data structures for string dictionary operations, that is, data str ..."
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Cited by 1 (0 self)
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Data warehouses are increasingly storing and managing large scale string data, and dealing with large volume of transactions that update and search string databases. Motivated by this context, we initiate the study of selfadjusting data structures for string dictionary operations, that is, data structures that are designed to be efficient on an entire sequence of operations rather than individual string operations. Furthermore, we study this problem in the external memory model where string data is too massive to be stored in main memory and has to reside in disks; each access to a disk page fetches B items, and the cost of the operations is the number of pages accessed. We show that given n strings S1, ..., Sn of total length P i jS i j = N , a sequence of m string searches S i 1 , S i 2 , ..., S i m takes O( P m j=1 ( jS i j j B ) + P n i=1 (n i log B m n i )) amortized expected I/Os, where n i is the number of times S i is queried. Inserting or deleting a string S takes O( jSj B + log B n) amortized expected I/Os. This result is the analog of what is known as the Static Optimality Theorem [17] proved by Sleator and Tarjan in their classic splay trees paper for a dictionary of numerical values; here, it has been generalized, for the first time to string data, to string operations, and to the external memory model. This performance is achieved not by traditional "splay" operations on search trees as in [17], but by designing a novel selfadjusting data structure based on the wellknown skip lists. In addition, we introduce the paradigm of using the main memory (or a part thereof) persistently across operations, in the manner of a cache, to further improve the performance of our selfadjusting skip list. This is quite reasonable in a...
unknown title
"... ABSTRACT A dictionary data structure supports efficient search, insert, and delete operations on n keys from a totally ordered universe. Redblack trees, 23 trees, AVL trees, skip lists and other classic data structures facilitate O(log n) time search, insert and deletes, matching the information t ..."
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ABSTRACT A dictionary data structure supports efficient search, insert, and delete operations on n keys from a totally ordered universe. Redblack trees, 23 trees, AVL trees, skip lists and other classic data structures facilitate O(log n) time search, insert and deletes, matching the information theoretic lower bound when access probabilities are uniform i.i.d. If access probabilities are nonuniform but still i.i.d., there are other weighted data structures such as Dtrees, biased search trees, splay trees and treaps which can achieve optimality. In many applications, however, the source of nonuniformity in access probabilities is locality of reference: examples include memory, cache, disk and buffer management and emerging applications in internetwork traffic management. In such applications, the access probability of any given key is not i.i.d., but decreases with idle time since the last access to the key.
Engineering Adaptive Software
, 1993
"... ions for Organizing Classes The key result of this grant is a new method to develop software based on delayed binding of methods to classes. The software becomes adaptive as illustrated later in the project description. Software becomes smaller and extensibility is improved. This research has resul ..."
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ions for Organizing Classes The key result of this grant is a new method to develop software based on delayed binding of methods to classes. The software becomes adaptive as illustrated later in the project description. Software becomes smaller and extensibility is improved. This research has resulted in the following publications: [LX93a, LX93c, Hol92, LHSLX92, Lie92a, LSLX92, LX93b, LSLX93, SLHS94, Lie94, Kes93, SL93b, SL93a, BH93, HLM93, LHX93, LZHL94] The research has resulted in a book and educational software, both to be published in 1994 by PWS Publishing Company. A significant number of graduate students have contributed to the research (as shown by the citations). Two women are important members of my research group. We have made a strong effort to disseminate our technology through teaching. I teach primarily software design and development classes at Northeastern where both undergraduate and graduate students get directly exposed to our research results. Propagation patte...