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Approximate Distance Labeling Schemes
, 2000
"... We consider the problem of labeling the nodes of an nnode graph G with short labels in such a way that the distance between any two nodes u; v of G can be approximated eciently (in constant time) by merely inspecting the labels of u and v, without using any other information. We develop such con ..."
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Cited by 46 (18 self)
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We consider the problem of labeling the nodes of an nnode graph G with short labels in such a way that the distance between any two nodes u; v of G can be approximated eciently (in constant time) by merely inspecting the labels of u and v, without using any other information. We develop such constant approximate distance labeling schemes for the classes of trees, bounded treewidth graphs, planar graphs, kchordal graphs, and graphs with a dominating pair (including for instance interval, permutation, and ATfree graphs). We also show lower bounds, and prove that most of our schemes are optimal in length of labels generated and in the quality of the approximation, leaving some open problems.
S.S.: Succinct indexes for strings, binary relations, and multilabeled trees
 In: Proc. SODA
, 2007
"... We define and design succinct indexes for several abstract data types (ADTs). The concept is to design auxiliary data structures that ideally occupy asymptotically less space than the informationtheoretic lower bound on the space required to encode the given data, and support an extended set of ope ..."
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Cited by 42 (11 self)
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We define and design succinct indexes for several abstract data types (ADTs). The concept is to design auxiliary data structures that ideally occupy asymptotically less space than the informationtheoretic lower bound on the space required to encode the given data, and support an extended set of operations using the basic operators defined in the ADT. The main advantage of succinct indexes as opposed to succinct (integrated data/index) encodings is that we make assumptions only on the ADT through which the main data is accessed, rather than the way in which the data is encoded. This allows more freedom in the encoding of the main data. In this paper, we present succinct indexes for various data types, namely strings, binary relations and multilabeled trees. Given the support for the interface of the ADTs of these data types, we can support various useful operations efficiently by constructing succinct indexes for them. When the operators in the ADTs are supported in constant time, our results are comparable to previous results, while allowing more flexibility in the encoding of the given data. Usingourtechniques,wedesignasuccinctencodingthatrepresentsastringoflengthnoveranalphabetof size σ using nHk(S)+lgσ·o(n)+O ( nlgσ lglglgσ) bits to support access/rank/select operations in o((lglgσ)1+ɛ) time, for any fixed constant ɛ> 0. We also design a succinct text index using nH0(S)+O ( nlgσ) bits that lglgσ
Canonical Decomposition of Outerplanar Maps and Application to Enumeration, Coding and Generation
, 2003
"... In this article we define a canonical decomposition of rooted outerplanar maps into a spanning tree and a list of edges. This decomposition, constructible in linear time, implies the existence of bijection between rooted outerplanar maps with n nodes and bicolored rooted ordered trees with n node ..."
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Cited by 12 (1 self)
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In this article we define a canonical decomposition of rooted outerplanar maps into a spanning tree and a list of edges. This decomposition, constructible in linear time, implies the existence of bijection between rooted outerplanar maps with n nodes and bicolored rooted ordered trees with n nodes where all the nodes of the last branch are colored white. As a consequence, for rooted outerplanar maps of n nodes, we derive: an enumeration formula, and an asymptotic of 2 3n (log n) ; an optimal data structure of asymptotically 3n bits, built in O(n) time, supporting adjacency and degree queries in worstcase constant time and neighbors query of a ddegree node in worstcase O(d) time...
Upper and Lower Bounds for Text Indexing Data Structures
"... c○Alexander Golynski 2007I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. (Alexander Golynski) The main go ..."
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Cited by 2 (1 self)
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c○Alexander Golynski 2007I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. (Alexander Golynski) The main goal of this thesis is to investigate the complexity of a variety of problems related to text indexing and text searching. We present new data structures that can be used as building blocks for fulltext indices which occupies minute space (FMindexes) and wavelet trees. These data structures also can be used to represent labeled trees and posting lists. Labeled trees are applied in XML documents, and posting lists in search engines. The main emphasis of this thesis is on lower bounds for timespace tradeoffs for the following problems: the rank/select problem, the problem of representing a string of balanced parentheses, the text retrieval problem, the problem of computing a permutation and its inverse, and the problem of representing a binary relation. These results are divided in two groups: lower bounds in the cell probe model and lower bounds in the indexing model.
Compressed String Dictionary Lookup with Edit Distance One
"... Abstract. In this paper we present different solutions for the problem of indexing a dictionary of strings in compressed space. Given a pattern P, the index has to report all the strings in the dictionary having edit distance at most one with P. Our first solution is able to solve queries in (almost ..."
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Cited by 1 (0 self)
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Abstract. In this paper we present different solutions for the problem of indexing a dictionary of strings in compressed space. Given a pattern P, the index has to report all the strings in the dictionary having edit distance at most one with P. Our first solution is able to solve queries in (almost optimal) O(P  + occ) time where occ is the number of strings in the dictionary having edit distance at most one with P. The space complexity of this solution is bounded in terms of the kth order entropy of the indexed dictionary. Our second solution further improves this space complexity at the cost of increasing the query time. 1