6,651 research outputs found
Parameterized Hash Functions
In this paper we describe a family of highly parameterized hash functions. This parameterization results in great flexibility between performance and security of the algorithm. The three basic functions, HaF-256, HaF-512 and HaF-1024 constitute this hash function family. Lengths of message digests are 256, 512 and 1024 bits respectively. The paper discusses the details of functions structure. The method used to generate function S-box is also described in detail
Variants of Constrained Longest Common Subsequence
In this work, we consider a variant of the classical Longest Common
Subsequence problem called Doubly-Constrained Longest Common Subsequence
(DC-LCS). Given two strings s1 and s2 over an alphabet A, a set C_s of strings,
and a function Co from A to N, the DC-LCS problem consists in finding the
longest subsequence s of s1 and s2 such that s is a supersequence of all the
strings in Cs and such that the number of occurrences in s of each symbol a in
A is upper bounded by Co(a). The DC-LCS problem provides a clear mathematical
formulation of a sequence comparison problem in Computational Biology and
generalizes two other constrained variants of the LCS problem: the Constrained
LCS and the Repetition-Free LCS. We present two results for the DC-LCS problem.
First, we illustrate a fixed-parameter algorithm where the parameter is the
length of the solution. Secondly, we prove a parameterized hardness result for
the Constrained LCS problem when the parameter is the number of the constraint
strings and the size of the alphabet A. This hardness result also implies the
parameterized hardness of the DC-LCS problem (with the same parameters) and its
NP-hardness when the size of the alphabet is constant
Improved Densification of One Permutation Hashing
The existing work on densification of one permutation hashing reduces the
query processing cost of the -parameterized Locality Sensitive Hashing
(LSH) algorithm with minwise hashing, from to merely ,
where is the number of nonzeros of the data vector, is the number of
hashes in each hash table, and is the number of hash tables. While that is
a substantial improvement, our analysis reveals that the existing densification
scheme is sub-optimal. In particular, there is no enough randomness in that
procedure, which affects its accuracy on very sparse datasets.
In this paper, we provide a new densification procedure which is provably
better than the existing scheme. This improvement is more significant for very
sparse datasets which are common over the web. The improved technique has the
same cost of for query processing, thereby making it strictly
preferable over the existing procedure. Experimental evaluations on public
datasets, in the task of hashing based near neighbor search, support our
theoretical findings
Fast Algorithms for Parameterized Problems with Relaxed Disjointness Constraints
In parameterized complexity, it is a natural idea to consider different
generalizations of classic problems. Usually, such generalization are obtained
by introducing a "relaxation" variable, where the original problem corresponds
to setting this variable to a constant value. For instance, the problem of
packing sets of size at most into a given universe generalizes the Maximum
Matching problem, which is recovered by taking . Most often, the
complexity of the problem increases with the relaxation variable, but very
recently Abasi et al. have given a surprising example of a problem ---
-Simple -Path --- that can be solved by a randomized algorithm with
running time . That is, the complexity of the
problem decreases with . In this paper we pursue further the direction
sketched by Abasi et al. Our main contribution is a derandomization tool that
provides a deterministic counterpart of the main technical result of Abasi et
al.: the algorithm for -Monomial
Detection, which is the problem of finding a monomial of total degree and
individual degrees at most in a polynomial given as an arithmetic circuit.
Our technique works for a large class of circuits, and in particular it can be
used to derandomize the result of Abasi et al. for -Simple -Path. On our
way to this result we introduce the notion of representative sets for
multisets, which may be of independent interest. Finally, we give two more
examples of problems that were already studied in the literature, where the
same relaxation phenomenon happens. The first one is a natural relaxation of
the Set Packing problem, where we allow the packed sets to overlap at each
element at most times. The second one is Degree Bounded Spanning Tree,
where we seek for a spanning tree of the graph with a small maximum degree
Encoding points on hyperelliptic curves over finite fields in deterministic polynomial time
We present families of (hyper)elliptic curve which admit an efficient
deterministic encoding function
Balanced Families of Perfect Hash Functions and Their Applications
The construction of perfect hash functions is a well-studied topic. In this
paper, this concept is generalized with the following definition. We say that a
family of functions from to is a -balanced -family
of perfect hash functions if for every , , the number
of functions that are 1-1 on is between and for some
constant . The standard definition of a family of perfect hash functions
requires that there will be at least one function that is 1-1 on , for each
of size . In the new notion of balanced families, we require the number
of 1-1 functions to be almost the same (taking to be close to 1) for
every such . Our main result is that for any constant , a
-balanced -family of perfect hash functions of size can be constructed in time .
Using the technique of color-coding we can apply our explicit constructions to
devise approximation algorithms for various counting problems in graphs. In
particular, we exhibit a deterministic polynomial time algorithm for
approximating both the number of simple paths of length and the number of
simple cycles of size for any
in a graph with vertices. The approximation is up to any fixed desirable
relative error
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