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Hash and displace: Efficient evaluation of minimal perfect hash functions
 In Workshop on Algorithms and Data Structures
, 1999
"... A new way of constructing (minimal) perfect hash functions is described. The technique considerably reduces the overhead associated with resolving buckets in twolevel hashing schemes. Evaluating a hash function requires just one multiplication and a few additions apart from primitive bit operations ..."
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Cited by 9 (1 self)
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A new way of constructing (minimal) perfect hash functions is described. The technique considerably reduces the overhead associated with resolving buckets in twolevel hashing schemes. Evaluating a hash function requires just one multiplication and a few additions apart from primitive bit operations. The number of accesses to memory is two, one of which is to a fixed location. This improves the probe performance of previous minimal perfect hashing schemes, and is shown to be optimal. The hash function description (“program”) for a set of size n occupies O(n) words, and can be constructed in expected O(n) time. 1
Dynamic Representations of Sparse Graphs
 In Proc. 6th International Workshop on Algorithms and Data Structures (WADS
, 1999
"... We present a linear space data structure for maintaining graphs with bounded arboricity  a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth  under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in wors ..."
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Cited by 8 (0 self)
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We present a linear space data structure for maintaining graphs with bounded arboricity  a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth  under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity.
Optimal spacetime dictionaries over an unbounded universe with flat implicit trees
, 2003
"... In the classical dictionary problem, a set of n distinct keys over an unbounded and ordered universe is maintained under insertions and deletions of individual keys while supporting search operations. An implicit dictionary has the additional constraint of occupying the space merely required by stor ..."
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Cited by 2 (1 self)
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In the classical dictionary problem, a set of n distinct keys over an unbounded and ordered universe is maintained under insertions and deletions of individual keys while supporting search operations. An implicit dictionary has the additional constraint of occupying the space merely required by storing the n keys, that is, exactly n contiguous words of space in total. All what is known is the starting position of the memory segment hosting the keys, as the rest of the information is implicitly encoded by a suitable permutation of the keys. This paper describes the
at implicit tree, which is the rst implicit dictionary requiring O(log n) time per search and update operation.
A New Tradeoff for Deterministic Dictionaries
, 2000
"... . We consider dictionaries over the universe U = f0; 1g w on a unitcost RAM with word size w and a standard instruction set. We present a linear space deterministic dictionary with membership queries in time (log log n) O(1) and updates in time (log n) O(1) , where n is the size of the se ..."
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. We consider dictionaries over the universe U = f0; 1g w on a unitcost RAM with word size w and a standard instruction set. We present a linear space deterministic dictionary with membership queries in time (log log n) O(1) and updates in time (log n) O(1) , where n is the size of the set stored. This is the rst such data structure to simultaneously achieve query time (log n) o(1) and update time O(2 (log n) c ) for a constant c < 1. 1 Introduction Among the most fundamental data structures is the dictionary. A dictionary stores a subset S of a universe U , oering membership queries of the form \x 2 S?". The result of a membership query is either 'no' or a piece of satellite data associated with x. Updates of the set are supported via insertion and deletion of single elements. Several performance measures are of interest for dictionaries: The amount of space used, the time needed to answer queries, and the time needed to perform updates. The most ecient dictionar...
Perfect Hash Families: Constructions and Applications
, 2003
"... Let A and B be nite sets with jAj = n and jBj = m. An (n; m;w)perfect hash family is a collection F of functions from A to B such that for any X A with jXj = w, there exists at least one f 2 F such that f is onetoone when restricted to X. Perfect hash families are basic combinatorial structures ..."
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Let A and B be nite sets with jAj = n and jBj = m. An (n; m;w)perfect hash family is a collection F of functions from A to B such that for any X A with jXj = w, there exists at least one f 2 F such that f is onetoone when restricted to X. Perfect hash families are basic combinatorial structures and they have played important roles in Computer Science in areas such as database management, operating systems, and compiler constructions. Such hash families are used for memory ecient storage and fast retrieval of items such as reserved words in programming languages, command names in interactive systems, or commonly used words in natural languages. More recently, perfect hash families have found numerous applications to cryptography, for example, to broadcast encryption schemes, secret sharing, key distribution patterns, visual cryptography, coverfree families and secure frameproof codes.
Lineartime algorithms to color topological graphs
, 2005
"... We describe a lineartime algorithm for 4coloring planar graphs. We indeed give an O(V + E + χ  + 1)time algorithm to Ccolor Vvertex Eedge graphs embeddable on a 2manifold M of Euler characteristic χ where C(M) is given by Heawood’s (minimax optimal) formula. Also we show how, in O(V + E) ..."
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We describe a lineartime algorithm for 4coloring planar graphs. We indeed give an O(V + E + χ  + 1)time algorithm to Ccolor Vvertex Eedge graphs embeddable on a 2manifold M of Euler characteristic χ where C(M) is given by Heawood’s (minimax optimal) formula. Also we show how, in O(V + E) time, to find the exact chromatic number of a maximal planar graph (one with E = 3V − 6) and a coloring achieving it. Finally, there is a lineartime algorithm to 5color a graph embedded on any fixed surface M except that an Mdependent constant number of vertices are left uncolored. All the algorithms are simple and practical and run on a deterministic pointer machine, except for planar graph 4coloring which involves enormous constant factors and requires an integer RAM with a random number generator. All of the algorithms mentioned so far are in the ultraparallelizable deterministic computational complexity class “NC. ” We also have more practical planar 4coloring algorithms that can run on pointer machines in O(V log V) randomized time and O(V) space, and a very simple deterministic O(V)time coloring algorithm for planar graphs which conjecturally uses 4 colors.
Protection—Proprietary rights General Terms Languages; Legal aspects,Security
"... Software piracy,Software protection,Watermarking Software watermarking is a tool used to combat software piracy by embedding identifying information into a program. Most existing proposals for software watermarking have the shortcoming that the mark can be destroyed via fairly straightforward semant ..."
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Software piracy,Software protection,Watermarking Software watermarking is a tool used to combat software piracy by embedding identifying information into a program. Most existing proposals for software watermarking have the shortcoming that the mark can be destroyed via fairly straightforward semanticspreserving code transformations. This paper introduces pathbased watermarking,a new approach to software watermarking based on the dynamic branching behavior of programs. The advantage of this technique is that errorcorrecting and tamperproofing techniquescanbeusedtomakepathbasedwatermarksresilient against a wide variety of attacks. Experimental results,usingbothJavabytecodeandIA32nativecode,indicate that even relatively large watermarks can be embedded into programs at modest cost. 1.