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- research-articleOctober 2023
A Cubic Algorithm for Computing the Hermite Normal Form of a Nonsingular Integer Matrix
ACM Transactions on Algorithms (TALG), Volume 19, Issue 4Article No.: 37, Pages 1–36https://doi.org/10.1145/3617996A Las Vegas randomized algorithm is given to compute the Hermite normal form of a nonsingular integer matrix A of dimension n. The algorithm uses quadratic integer multiplication and cubic matrix multiplication and has running time bounded by O(n3 (log n +...
- research-articleJuly 2019
Faster Carry Bit Computation for Adder Circuits with Prescribed Arrival Times
ACM Transactions on Algorithms (TALG), Volume 15, Issue 4Article No.: 45, Pages 1–23https://doi.org/10.1145/3340321We consider the fundamental problem of constructing fast circuits for the carry bit computation in binary addition. Up to a small additive constant, the carry bit computation reduces to computing an And-Or path, i.e., a formula of type t0 ∧ (t1 ∨ (t2 ∧ (...
- research-articleAugust 2018
Deterministic Parallel Algorithms for Fooling Polylogarithmic Juntas and the Lovász Local Lemma
ACM Transactions on Algorithms (TALG), Volume 14, Issue 4Article No.: 47, Pages 1–24https://doi.org/10.1145/3230651Many randomized algorithms can be derandomized efficiently using either the method of conditional expectations or probability spaces with low (almost-) independence. A series of papers, beginning with Luby (1993) and continuing with Berger and Rompel (...
- research-articleAugust 2018
Batched Point Location in SINR Diagrams via Algebraic Tools
ACM Transactions on Algorithms (TALG), Volume 14, Issue 4Article No.: 41, Pages 1–29https://doi.org/10.1145/3209678The SINR (Signal to Interference plus Noise Ratio) model for the quality of wireless connections has been the subject of extensive recent study. It attempts to predict whether a particular transmitter is heard at a specific location, in a setting ...
- research-articleSeptember 2016
Tabulating Pseudoprimes and Tabulating Liars
ACM Transactions on Algorithms (TALG), Volume 13, Issue 1Article No.: 4, Pages 1–14https://doi.org/10.1145/2957759This article explores the asymptotic complexity of two problems related to the Miller-Rabin-Selfridge primality test. The first problem is to tabulate strong pseudoprimes to a single fixed base a. It is now proven that tabulating up to x requires O(x) ...
- research-articleApril 2016
Approximation Algorithms for Stochastic Submodular Set Cover with Applications to Boolean Function Evaluation and Min-Knapsack
ACM Transactions on Algorithms (TALG), Volume 12, Issue 3Article No.: 42, Pages 1–28https://doi.org/10.1145/2876506We present a new approximation algorithm for the stochastic submodular set cover (SSSC) problem called adaptive dual greedy. We use this algorithm to obtain a 3-approximation algorithm solving the stochastic Boolean function evaluation (SBFE) problem ...
- research-articleFebruary 2016
Computing the Distance between Piecewise-Linear Bivariate Functions
ACM Transactions on Algorithms (TALG), Volume 12, Issue 1Article No.: 3, Pages 1–13https://doi.org/10.1145/2847257We consider the problem of computing the distance between two piecewise-linear bivariate functions f and g defined over a common domain M, induced by the L2 norm—that is, ‖ f - g‖2 = √∫M(f - g)2. If f is defined by linear interpolation over a ...
- research-articleAugust 2014
Real-Time Streaming String-Matching
ACM Transactions on Algorithms (TALG), Volume 10, Issue 4Article No.: 22, Pages 1–12https://doi.org/10.1145/2635814This article presents a real-time randomized streaming string-matching algorithm that uses O(log m) space. The algorithm only makes one-sided small probability false-positive errors, possibly reporting phantom occurrences of the pattern, but never ...
- research-articleOctober 2013
On the matrix berlekamp-massey algorithm
ACM Transactions on Algorithms (TALG), Volume 9, Issue 4Article No.: 33, Pages 1–24https://doi.org/10.1145/2500122We analyze the Matrix Berlekamp/Massey algorithm, which generalizes the Berlekamp/Massey algorithm [Massey 1969] for computing linear generators of scalar sequences. The Matrix Berlekamp/Massey algorithm computes a minimal matrix generator of a linearly ...
- research-articleJuly 2012
Assignment problem in content distribution networks: Unsplittable hard-capacitated facility location
ACM Transactions on Algorithms (TALG), Volume 8, Issue 3Article No.: 20, Pages 1–19https://doi.org/10.1145/2229163.2229164In a Content Distribution Network (CDN), there are m servers storing the data; each of them has a specific bandwidth. All the requests from a particular client should be assigned to one server because of the routing protocol used. The goal is to ...
- research-articleDecember 2009
The Knuth-Yao quadrangle-inequality speedup is a consequence of total monotonicity
ACM Transactions on Algorithms (TALG), Volume 6, Issue 1Article No.: 17, Pages 1–22https://doi.org/10.1145/1644015.1644032There exist several general techniques in the literature for speeding up naive implementations of dynamic programming. Two of the best known are the Knuth-Yao quadrangle inequality speedup and the SMAWK algorithm for finding the row-minima of totally ...
- research-articleJuly 2008
Testing Euclidean minimum spanning trees in the plane
ACM Transactions on Algorithms (TALG), Volume 4, Issue 3Article No.: 31, Pages 1–23https://doi.org/10.1145/1367064.1367071Given a Euclidean graph G over a set P of n points in the plane, we are interested in verifying whether G is a Euclidean minimum spanning tree (EMST) of P or G differs from it in more than ϵ n edges. We assume that G is given in adjacency list ...
- articleNovember 2007
Optimal parallel selection
ACM Transactions on Algorithms (TALG), Volume 3, Issue 4Pages 38–eshttps://doi.org/10.1145/1290672.1290675We present an optimal parallel selection algorithm on the EREW PRAM. This algorithm runs in O(log n) time with n/log n processors. This complexity matches the known lower bound for parallel selection on the EREW PRAM model. We therefore close this ...
- articleMay 2007
An algorithm for deciding zero equivalence of nested polynomially recurrent sequences
ACM Transactions on Algorithms (TALG), Volume 3, Issue 2Pages 18–eshttps://doi.org/10.1145/1240233.1240241We introduce the class of nested polynomially recurrent sequences which includes a large number of sequences that are of combinatorial interest. We present an algorithm for deciding zero equivalence of these sequences, thereby providing a new algorithm ...
- articleMay 2007
Multiplierless multiple constant multiplication
ACM Transactions on Algorithms (TALG), Volume 3, Issue 2Pages 11–eshttps://doi.org/10.1145/1240233.1240234A variable can be multiplied by a given set of fixed-point constants using a multiplier block that consists exclusively of additions, subtractions, and shifts. The generation of a multiplier block from the set of constants is known as the multiple ...
- articleJuly 2005
Fast sparse matrix multiplication
ACM Transactions on Algorithms (TALG), Volume 1, Issue 1Pages 2–13https://doi.org/10.1145/1077464.1077466Let A and B two n×n matrices over a ring R (e.g., the reals or the integers) each containing at most m nonzero elements. We present a new algorithm that multiplies A and B using O(m0.7n1.2+n2+o(1)) algebraic operations (i.e., multiplications, additions ...