The purpose of this paper is to present a best proximity point theorems through rational expression for a combination of contraction condition, Kannan and Chatterjea nonlinear cyclic contraction in what we call MT-K and MT-C rational cyclic contraction. Some best proximity point theorems for a mapping satisfy these conditions have been established in metric spaces. We also give some examples to...

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 ...

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...

Farach, Kannan and Warnow (1995) have defined Problem MCA (matrix completion to additive) and proved it to be NP-complete: given a partial dissimilarity d on a finite set X , does there exist a tree metric extending d to all pairs of elements of X . We use a previously described simple method of phylogenetic reconstruction, and its extension to partial dissimilarities, to characterize some clas...

We present an O(n4)-time algorithm for the following problem: Given a set of items with known access frequencies, find the optimal binary search tree under the realistic assumption that each comparison can only result in a two-way decision: either an equality comparison or a less-than comparisons. This improves the best known result of O(n5) time, which is based on split tree algorithms. Our al...