The paper presents a new fast k-ary reduction for integer GCD. It enjoys powerful properties and improves on the running time of the quite similar integer GCD algorithm of Kannan et al. Our k-ary reduction also improves on Sorenson's k-ary reductionn14] and thus favorably matches We-ber's algorithmm15]. More generally, the fast k-ary reduction also provides a basic tool for almost all the best ...

Independent Component Analysis (ICA), a well-known approach in statistics, assumes that data is generated by applying an affine transformation of a fully independent set of random variables, and aims to recover the orthogonal basis corresponding to the independent random variables. We consider a generalization of ICA, wherein the data is generated as an affine transformation applied to a produc...

The study of fixed points of single-valued self-mappings or multivalued self-mappings satisfying certain contraction conditions has a great majority of results inmetric fixed point theory. All these results are mainly generalizations of Banach contraction principle. The Banach contraction principle guarantees the existence and uniqueness of fixed points of certain self-maps in complete metric s...

Disclosures: M.C. Mendoza: None. K. Sonn: None. S.S. Bellary: None. A. Kannan: None. G. Singh: None. C. Park: None. S.R. Stock: None. E.L. Hsu: 2; Medtronic, Stryker, Pioneer Surgical, Globus, SpineSmith, Lifenet, AONA, Synthes/DePuy, Bioventus. 3B; Stryker, Zimmer, Medtronic, Pioneer Surgical, Terumo, Spinesmith. W. Hsu: 2; Medtronic, Stryker, Pioneer Surgical, Globus, SpineSmith, Lifenet, AON...

In this paper, we propose a new phase-based enumeration algorithm based on two interesting and useful observations for y-sparse representations of short lattice vectors in lattices from SVP challenge benchmarks[24]. Experimental results show that the phase-based algorithm greatly outperforms other famous enumeration algorithms in running time and achieves higher dimensions, like the Kannan-Helf...

We describe a simple way of partitioning a planar graph into three edge-disjoint forests in O(n log n) time, where n is the number of its vertices. We can use this partition in Kannan et al.‘s graph representation (1992) to label the planar graph vertices so that any two vertices’ adjacency can be tested locally by comparing their names in constant time.

The Orbit problem is defined as follows: Given a matrix A ∈ Q and vectors x,y ∈ Q, does there exist a non-negative integer i such that Ax = y. This problem was shown to be in deterministic polynomial time by Kannan and Lipton in [8]. In this paper we place the problem in the logspace counting hierarchy GapLH. We also show that the problem is hard for L under NC-many-one reductions.

The aim of this paper is to extend the Kannan fixed point theorem from single-valued self mappings T : X → X to mappings F : X3 → X satisfying a Prešić-Kannan type contractive condition: d (F (x, y, z) , F (y, z, u)) ≤ k 8 [d (x, F (x, y, z)) + d (y, F (y, x, y))+ +d (z, F (z, y, x)) + d (y, F (y, z, u)) + d (z, F (z, y, z)) + d (u, F (u, z, y))], or a Prešić-Chatterjea type contractive conditi...