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46
Compact Suffix Array
, 2000
"... Suffix array is a data structure that can be used to index a large text le so that queries of its content can be answered quickly. Basically a suffix array is an array of all suffixes of the text in the lexicographic order. Whether or not a word occurs in the text can be answered in logarithmic time ..."
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Cited by 32 (10 self)
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Suffix array is a data structure that can be used to index a large text le so that queries of its content can be answered quickly. Basically a suffix array is an array of all suffixes of the text in the lexicographic order. Whether or not a word occurs in the text can be answered in logarithmic time by binary search over the suffix array. In this work we present a method to compress a suffix array such that the search time remains logarithmic. Our experiments show that in some cases a suffix array can be compressed by our method such that the total space requirement is about half of the original.
Compact Routing Tables for Graphs of Bounded Genus
, 2000
"... This paper deals with compact shortest path routing tables on weighted graphs with n nodes. For planar graphs we show how to construct in linear time shortest path routing tables that require 8n + o(n) bits per node, and O(log 2+ n) bitoperations per node to extract the route, for any constant > 0. ..."
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Cited by 31 (13 self)
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This paper deals with compact shortest path routing tables on weighted graphs with n nodes. For planar graphs we show how to construct in linear time shortest path routing tables that require 8n + o(n) bits per node, and O(log 2+ n) bitoperations per node to extract the route, for any constant > 0. We obtain the same bounds for graphs of crossingedge number bounded by o(n= log n), and we generalize for graphs of genus bounded by > 0 yielding a size of n log +O(n) bits per node. Actually we prove a sharp upper bound of 2n log k +O(n) for graphs of pagenumber k, and a lower bound of n log k o(n log k) bits. These results are obtained by the use of dominating sets, compact coding of noncrossing partitions, and kpage representation of graphs.
The Cell Probe Complexity of Succinct Data Structures
 In Automata, Languages and Programming, 30th International Colloquium (ICALP 2003
, 2003
"... We show lower bounds in the cell probe model for the redundancy/query time tradeoff of solutions to static data structure problems. ..."
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Cited by 30 (0 self)
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We show lower bounds in the cell probe model for the redundancy/query time tradeoff of solutions to static data structure problems.
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
Succinct Dynamic Data Structures
"... We develop succinct data structures to represent (i) a sequence of values to support partial sum and select queries and update (changing values) and (ii) a dynamic array consisting of a sequence of elements which supports insertion, deletion and access of an element at any given index. For the parti ..."
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Cited by 25 (2 self)
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We develop succinct data structures to represent (i) a sequence of values to support partial sum and select queries and update (changing values) and (ii) a dynamic array consisting of a sequence of elements which supports insertion, deletion and access of an element at any given index. For the partial sums problem...
Compressed data structures: dictionaries and dataaware measures
 In Proc. 5th International Workshop on Experimental Algorithms (WEA
, 2006
"... Abstract. We propose measures for compressed data structures, in which space usage is measured in a dataaware manner. In particular, we consider the fundamental dictionary problem on set data, where the task is to construct a data structure to represent a set S of n items out of a universe U = {0,. ..."
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Cited by 23 (2 self)
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Abstract. We propose measures for compressed data structures, in which space usage is measured in a dataaware manner. In particular, we consider the fundamental dictionary problem on set data, where the task is to construct a data structure to represent a set S of n items out of a universe U = {0,..., u − 1} and support various queries on S. We use a wellknown dataaware measure for set data called gap to bound the space of our data structures. We describe a novel dictionary structure taking gap+O(n log(u/n) / log n)+O(n log log(u/n)) bits. Under the RAM model, our dictionary supports membership, rank, select, and predecessor queries in nearly optimal time, matching the time bound of Andersson and Thorup’s predecessor structure [AT00], while simultaneously improving upon their space usage. Our dictionary structure uses exactly gap bits in the leading term (i.e., the constant factor is 1) and answers queries in nearoptimal time. When seen from the worst case perspective, we present the first O(n log(u/n))bit dictionary structure which supports these queries in nearoptimal time under RAM model. We also build a dictionary which requires the same space and supports membership, select, and partial rank queries even more quickly in O(log log n) time. To the best of our knowledge, this is the first of a kind result which achieves dataaware space usage and retains nearoptimal time. 1
Low Redundancy in Static Dictionaries with O(1) Worst Case Lookup Time
 IN PROCEEDINGS OF THE 26TH INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP '99
, 1999
"... A static dictionary is a data structure for storing subsets of a nite universe U , so that membership queries can be answered efficiently. We study this problem in a unit cost RAM model with word size (log jU j), and show that for nelement subsets, constant worst case query time can be obtained us ..."
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Cited by 21 (5 self)
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A static dictionary is a data structure for storing subsets of a nite universe U , so that membership queries can be answered efficiently. We study this problem in a unit cost RAM model with word size (log jU j), and show that for nelement subsets, constant worst case query time can be obtained using B +O(log log jU j) + o(n) bits of storage, where B = dlog 2 jUj n e is the minimum number of bits needed to represent all such subsets. For jU j = n log O(1) n the dictionary supports constant time rank queries.
Compact Representations Of Ordered Sets
, 2004
"... We consider the problem of e#ciently representing sets S of size n from an ordered universe U = . . . , m1}. Given any ordered dictionary structure (or comparisonbased ordered set structure) D that uses O(n) pointers, we demonstrate a simple blocking technique that produces an ordered set struc ..."
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Cited by 21 (3 self)
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We consider the problem of e#ciently representing sets S of size n from an ordered universe U = . . . , m1}. Given any ordered dictionary structure (or comparisonbased ordered set structure) D that uses O(n) pointers, we demonstrate a simple blocking technique that produces an ordered set structure supporting the same operations in the same time bounds but with O(n log n ) bits. This is within a constant factor of the informationtheoretic lower bound. We assume the unit cost RAM model with word size #ze U ) and a table of size O(m m) bits, for some constant # > 0. The time bound for our operations contains a factor of 1/#. We present
Low Redundancy in Dictionaries with O(1) Worst Case Lookup Time
 IN PROC. 26TH INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP
, 1998
"... A static dictionary is a data structure for storing subsets of a finite universe U , so that membership queries can be answered efficiently. We study this problem in a unit cost RAM model with word size ze jU j), and show that for nelement subsets, constant worst case query time can be obtain ..."
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Cited by 18 (0 self)
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A static dictionary is a data structure for storing subsets of a finite universe U , so that membership queries can be answered efficiently. We study this problem in a unit cost RAM model with word size ze jU j), and show that for nelement subsets, constant worst case query time can be obtained using B +O(log log jU j) + o(n) bits of storage, where B = dlog jU j e is the minimum number of bits needed to represent all such subsets. The solution for dense subsets uses B + O( jU j log log jU j log jU j ) bits of storage, and supports constant time rank queries. In a dynamic setting, allowing insertions and deletions, our techniques give an O(B) bit space usage.
Cuckoo hashing: Further analysis
, 2003
"... We consider cuckoo hashing as proposed by Pagh and Rodler in 2001. We show that the expected construction time of the hash table is O(n) as long as the two open addressing tables are each of size at least (1 #)n,where#>0andn is the number of data points. Slightly improved bounds are obtained for ..."
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Cited by 17 (1 self)
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We consider cuckoo hashing as proposed by Pagh and Rodler in 2001. We show that the expected construction time of the hash table is O(n) as long as the two open addressing tables are each of size at least (1 #)n,where#>0andn is the number of data points. Slightly improved bounds are obtained for various probabilities and constraints. The analysis rests on simple properties of branching processes.