Results 1 
9 of
9
Fast computation of common left multiples of linear ordinary differential operators
 in Proceedings of ISSAC’12
, 2012
"... We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyse the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs. We propose a new algorithm that recasts the LCLM computation in a li ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyse the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs. We propose a new algorithm that recasts the LCLM computation in a linear algebra problem on a polynomial matrix. This algorithm yields sharp bounds on the coefficient degrees of the LCLM, improving by one order of magnitude the best bounds obtained using previous algorithms. The complexity of the new algorithm is almost optimal, in the sense that it nearly matches the arithmetic size of the output. Categories and Subject Descriptors:
Destination Prediction by SubTrajectory Synthesis and Privacy Protection Against Such Prediction
"... Abstract — Destination prediction is an essential task for many emerging location based applications such as recommending sightseeing places and targeted advertising based on destination. A common approach to destination prediction is to derive the probability of a location being the destination bas ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract — Destination prediction is an essential task for many emerging location based applications such as recommending sightseeing places and targeted advertising based on destination. A common approach to destination prediction is to derive the probability of a location being the destination based on historical trajectories. However, existing techniques using this approach suffer from the “data sparsity problem”, i.e., the available historical trajectories is far from being able to cover all possible trajectories. This problem considerably limits the number of query trajectories that can obtain predicted destinations. We propose a novel method named SubTrajectory Synthesis (SubSyn) algorithm to address the data sparsity problem. SubSyn algorithm first decomposes historical trajectories into subtrajectories comprising two neighbouring locations, and then connects the subtrajectories into “synthesised ” trajectories. The number of query trajectories that can have predicted destinations is exponentially increased by this means. Experiments based on real datasets show that SubSyn algorithm can predict destinations for up to ten times more query trajectories than a baseline algorithm while the SubSyn prediction algorithm runs over two orders of magnitude faster than the baseline algorithm. In this paper, we also consider the privacy protection issue in case an adversary uses SubSyn algorithm to derive sensitive location information of users. We propose an efficient algorithm to select a minimum number of locations a user has to hide on her trajectory in order to avoid privacy leak. Experiments also validate the high efficiency of the privacy protection algorithm. I.
Acknowledgments
"... The investigations were performed at the Centrum Wiskunde & Informatica (CWI) and were supported by Vici grant 639.023.302 from the Netherlands Organization for Scientific Research (NWO). ..."
Abstract
 Add to MetaCart
The investigations were performed at the Centrum Wiskunde & Informatica (CWI) and were supported by Vici grant 639.023.302 from the Netherlands Organization for Scientific Research (NWO).
unknown title
, 2012
"... These notes are based on a lecture given at the Toronto Student Seminar on February 9, 2012. The material is taken mostly from the classic paper by Coppersmith and Winograd [CW]. Other sources are §15.7 of Algebraic Complexity Theory [ACT], Stothers’s thesis [Sto] and V. Williams’s recent paper [Wil ..."
Abstract
 Add to MetaCart
These notes are based on a lecture given at the Toronto Student Seminar on February 9, 2012. The material is taken mostly from the classic paper by Coppersmith and Winograd [CW]. Other sources are §15.7 of Algebraic Complexity Theory [ACT], Stothers’s thesis [Sto] and V. Williams’s recent paper [Wil]. Starred sections are the ones we didn’t have time to cover. We present three different algorithms, all taken from [CW], in rapid succession. All these algorithms are based on Strassen’s groundbreaking laser method. Strassen’s original ideas are described in the appendix.
COMPLEXITY OF QUANTUM FIELD THEORIES
"... Abstract. Quantum field theories (QFTs) reconcile special relativity and quantum mechanics. We discuss the computational complexity of these theories. In particular, we present the recentlydevised algorithm of Jordan, Lee, and Preskill which gives an efficient simulation of φ 4 theory in d = 1, 2, ..."
Abstract
 Add to MetaCart
Abstract. Quantum field theories (QFTs) reconcile special relativity and quantum mechanics. We discuss the computational complexity of these theories. In particular, we present the recentlydevised algorithm of Jordan, Lee, and Preskill which gives an efficient simulation of φ 4 theory in d = 1, 2, and 3 spatial dimensions with a nonrelativistic quantum computer, allowing for the computation of scattering probabilities. The algorithm’s run time is polynomial in the desired precision, the number of incoming particles, and their energy. The fastest known classical algorithm is exponentially slower when we desire high precision or when the φ 4 coupling constant is large. 1.
A fast solver for a class of linear systems ∗
"... The solution of linear systems is a problem of fundamental theoretical importance but also one with a myriad of applications in numerical mathematics, engineering and science. Linear systems that are generated by realworld applications frequently fall into special classes. Recent research led to a ..."
Abstract
 Add to MetaCart
The solution of linear systems is a problem of fundamental theoretical importance but also one with a myriad of applications in numerical mathematics, engineering and science. Linear systems that are generated by realworld applications frequently fall into special classes. Recent research led to a fast algorithm for solving symmetric diagonally dominant (SDD) linear systems. We give an overview of this solver and survey the underlying notions and tools from algebra, probability and graph algorithms. We also discuss some of the many and diverse applications of SDD solvers. 1.
1 Finding and listing induced paths and cycles 2
, 2012
"... Many recognition problems for special classes of graphs and cycles can be reduced to finding and listing induced paths and cycles in a graph. We design algorithms to list all P3’s in O(m1.5 + p3(G)) time, and for k ≥ 4 all Pk’s in O(nk−1 +pk(G)+k·ck(G)) time, where pk(G), respectively, ck(G), are th ..."
Abstract
 Add to MetaCart
Many recognition problems for special classes of graphs and cycles can be reduced to finding and listing induced paths and cycles in a graph. We design algorithms to list all P3’s in O(m1.5 + p3(G)) time, and for k ≥ 4 all Pk’s in O(nk−1 +pk(G)+k·ck(G)) time, where pk(G), respectively, ck(G), are the number of Pk’s, respectively, Ck’s, of a graph G. We also provide an algorithm to find a Pk, k ≥ 5, in time O(k!!·m (k−1)/2) if k is odd, and O(k!! · nm (k/2)−1) if k is even. As applications of our findings, we give algorithms to recognize quasitriangulated graphs and brittle graphs. Our algorithms ’ time bounds are incomparable with previously known algorithms.
Algorithms for the universal decomposition algebra
"... Let k be a field and let f ∈ k [T] be a polynomial of degree n. The universal decomposition algebra A is the quotient of k [X1,..., Xn] by the ideal of symmetric relations (those polynomials that vanish on all permutations of the roots of f). We show how to obtain efficient algorithms to compute in ..."
Abstract
 Add to MetaCart
Let k be a field and let f ∈ k [T] be a polynomial of degree n. The universal decomposition algebra A is the quotient of k [X1,..., Xn] by the ideal of symmetric relations (those polynomials that vanish on all permutations of the roots of f). We show how to obtain efficient algorithms to compute in A. We use a univariate representation of A, i.e. an isomorphism of the form A ≃ k[T]/Q(T), since in this representation, arithmetic operations in A are known to be quasioptimal. We give details for two related algorithms, to find the isomorphism above, and to compute the characteristic polynomial of any element of A.
Cryptography from tensor problems
, 2012
"... This manuscript describes a proposal for a new trapdoor oneway function of the multivariatequadratic type. It was first posted to the IACR preprint server in May 2012. Subsequently, Enrico Thomae and Christopher Wolf were able to to determine that a smallminors MinRank attack works against this s ..."
Abstract
 Add to MetaCart
This manuscript describes a proposal for a new trapdoor oneway function of the multivariatequadratic type. It was first posted to the IACR preprint server in May 2012. Subsequently, Enrico Thomae and Christopher Wolf were able to to determine that a smallminors MinRank attack works against this scheme. I would like to thank them for their close study of the proposal. The manuscript follows as originally posted, with the addition of a few references and a brief description of the successful attack (end of Section 4.1). Keywords: cryptography. Multivariate quadratic cryptosystem, MinRank, tensor rank, postquantum 1