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11
Marked Ancestor Problems
, 1998
"... Consider a rooted tree whose nodes can be marked or unmarked. Given a node, we want to find its nearest marked ancestor. This generalises the wellknown predecessor problem, where the tree is a path. ..."
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Cited by 52 (7 self)
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Consider a rooted tree whose nodes can be marked or unmarked. Given a node, we want to find its nearest marked ancestor. This generalises the wellknown predecessor problem, where the tree is a path.
Cell probe complexity  a survey
 In 19th Conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS), 1999. Advances in Data Structures Workshop
"... The cell probe model is a general, combinatorial model of data structures. We give a survey of known results about the cell probe complexity of static and dynamic data structure problems, with an emphasis on techniques for proving lower bounds. 1 ..."
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Cited by 29 (0 self)
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The cell probe model is a general, combinatorial model of data structures. We give a survey of known results about the cell probe complexity of static and dynamic data structure problems, with an emphasis on techniques for proving lower bounds. 1
Hardness Results for Dynamic Problems by Extensions of Fredman and Saks' Chronogram Method
 In Proc. 25th Int. Coll. Automata, Languages, and Programming, number 1443 in Lecture Notes in Computer Science
, 1998
"... We introduce new models for dynamic computation based on the cell probe model of Fredman and Yao. We give these models access to nondeterministic queries or the right answer ±1 as an oracle. We prove that for the dynamic partial sum problem, these new powers do not help, the problem retains i ..."
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Cited by 9 (4 self)
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We introduce new models for dynamic computation based on the cell probe model of Fredman and Yao. We give these models access to nondeterministic queries or the right answer ±1 as an oracle. We prove that for the dynamic partial sum problem, these new powers do not help, the problem retains its lower bound of Omega (log n/ log log n). From...
New Lower Bound Techniques For Dynamic Partial Sums and Related Problems
 SIAM Journal on Computing
, 2003
"... We study the complexity of the dynamic partial sum problem in the cellprobe model. We give the model access to nondeterministic queries and prove that the problem remains hard. We give the model access to the right answer as an oracle and prove that the problem remains hard. This suggests which kin ..."
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Cited by 8 (1 self)
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We study the complexity of the dynamic partial sum problem in the cellprobe model. We give the model access to nondeterministic queries and prove that the problem remains hard. We give the model access to the right answer as an oracle and prove that the problem remains hard. This suggests which kind of information is hard to maintain. From these results, we derive a number of lower bounds for dynamic algorithms and data structures: We prove lower bounds for dynamic algorithms for existential range queries, reachability in directed graphs, planarity testing, planar point location, incremental parsing, and fundamental data structure problems like maintaining the majority of the prefixes of a string of bits. We prove a lower bound for reachability in grid graphs in terms of the graph's width. We characterize the complexity of maintaining the value of any symmetric function on the prefixes of a bit string. Keywords. cellprobe model, partial sum, dynamic algorithm, data structure AMS subject classifications. 68Q17, 68Q10, 68Q05, 68P05
Pattern Matching in Dynamic Texts
, 2000
"... Pattern matching is the problem of nding all occurrences of a pattern in a text. In a dynamic setting the problem is to support pattern matching in a text which can be manipulated online, i.e., the usual situation in text editing. We present a data structure that supports insertions and deletions ..."
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Cited by 6 (0 self)
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Pattern matching is the problem of nding all occurrences of a pattern in a text. In a dynamic setting the problem is to support pattern matching in a text which can be manipulated online, i.e., the usual situation in text editing. We present a data structure that supports insertions and deletions of characters and movements of arbitrary large blocks within a text in O(log 2 n log log n log n) time per operation. Furthermore a search for a pattern P in the text is supported in time O(log n log log n + occ + jP j), where occ is the number of occurrences to be reported. An ingredient in our solution to the above main result is a data structure for the dynamic string equality problem introduced by Mehlhorn, Sundar and Uhrig. As a secondary result we give almost quadratic better time bounds for this problem which in addition to keeping polylogarithmic factors low for our main result also improves the complexity for several other problems.
THE DYNAMIC COMPLEXITY OF FORMAL LANGUAGES
 STACS
, 2009
"... The paper investigates the power of the dynamic complexity classes DynFO, DynQF and DynPROP over string languages. The latter two classes contain problems that can be maintained using quantifierfree firstorder updates, with and without auxiliary functions, respectively. It is shown that the lang ..."
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Cited by 1 (0 self)
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The paper investigates the power of the dynamic complexity classes DynFO, DynQF and DynPROP over string languages. The latter two classes contain problems that can be maintained using quantifierfree firstorder updates, with and without auxiliary functions, respectively. It is shown that the languages maintainable in DynPROP exactly are the regular languages, even when allowing arbitrary precomputation. This enables lower bounds for DynPROP and separates DynPROP from DynQF and DynFO. Further, it is shown that any contextfree language can be maintained in DynFO and a number of specific contextfree languages, for example all Dycklanguages, are maintainable in DynQF. Furthermore, the dynamic complexity of regular tree languages is investigated and some results concerning arbitrary structures are obtained: there exist firstorder definable properties which are not maintainable in DynPROP. On the other hand any existential firstorder property can be maintained in DynQF when allowing precomputation.
Complexity of UnionSplitFind Problems
, 2007
"... In this thesis, we investigate various interpretations of the UnionSplitFind problem, an extension of the classic UnionFind problem. In the UnionSplitFind problem, we maintain disjoint sets of ordered elements subject to the operations of constructing singleton sets, merging two sets together, ..."
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In this thesis, we investigate various interpretations of the UnionSplitFind problem, an extension of the classic UnionFind problem. In the UnionSplitFind problem, we maintain disjoint sets of ordered elements subject to the operations of constructing singleton sets, merging two sets together, splitting a set by partitioning it around a specified value, and finding the set that contains a given element. The different interpretations of this problem arise from the different assumptions made regarding when sets can be merged and any special properties the sets may have. We define and analyze the Interval, Cyclic, Ordered, and General UnionSplitFind problems. Previous work implies optimal solutions to the Interval and Ordered UnionSplitFind problems and an Ω(log n / log log n) lower bound for the Cyclic UnionSplitFind problem in the cellprobe model. We present a new data
DYNAMIC PATTERN MATCHING
"... ABSTRACT. Pattern matching is the problem of finding all occurrences of a pattern in a text. For a long period of time significant progress has been made in solving increasingly more generalized and dynamic versions of this problem. In this paper we introduce a fully dynamic generalization of the pa ..."
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ABSTRACT. Pattern matching is the problem of finding all occurrences of a pattern in a text. For a long period of time significant progress has been made in solving increasingly more generalized and dynamic versions of this problem. In this paper we introduce a fully dynamic generalization of the pattern matching problem. We show how to maintain a family of strings under split and concatenation operations. Given a string in the family, all occurrences of it in the family are reported within time occ time, where is the total size of the strings and occ is the number of occurrences. Updates are performed in time. These bounds are competitive or improve former results for less generalized versions of the problem. As an intermediate result of independent interest, we provide an almost quadratic improvement of the time bounds for the dynamic string equality problem due to Mehlhorn, Sundar and Uhrig.
and
, 2001
"... All rights reserved. Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. ISSN 1600–6100 ISBN 8779490123 ..."
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All rights reserved. Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. ISSN 1600–6100 ISBN 8779490123