We give a polynomial time Turing reduction from the γ √ napproximate closest vector problem on a lattice of dimension n to a γapproximate oracle for the shortest vector problem. This is an improvement over a reduction by Kannan, which achieved γn 3

In this paper, the concept of cyclic (φ− ψ)-Kannan and cyclic (φ− ψ)-Chatterjea contractions, and fixed point theorems for these types of mappings in the context of complete metric spaces have been introduced. The results proved here extend some fixed point theorems in the literature.

We give some extensions of the beautiful 1968 fixed point theorem Maia [Maia, M. G. Un’osservazione sulle contrazioni metriche. (Italian) Rend. Sem. Mat. Univ. Padova 40 (1968), 139–143] to three classes enriched contractive mappings in Banach spaces: contractions, Kannan contractions and Ćirić-Reich-Rus contractions.

This note extends a recent result of Kannan, Tetali and Vempala to completely solve, via a simple proof, the problem of random generation of a labeled tournament with a given score vector. The proof uses the method of path coupling applied to an appropriate Markov chain on the set of labeled tournaments with the same score vector. MRS: 65C05, 05C20.

Bourgain and Yehudayoff recently constructed O(1)-monotone bipartite expanders. By combining this result with a generalisation of the unraveling method of Kannan, we construct 3-monotone bipartite expanders, which is best possible. We then show that the same graphs admit 3-page book embeddings, 2-queue layouts, 4-track layouts, and have simple thickness 2. All these results are best possible.

In this paper we prove that two local conditions involving the degrees and co-degrees in a graph can be used to determine whether a given vertex partition is Frieze–Kannan-regular. With a more refined version of these two local conditions we provide a deterministic algorithm that obtains a Frieze–Kanan-regular partition of any graph G in time O(|V (G)|).

In this paper, we introduce the concepts of qpb-cyclic-Banach contraction mapping, qpb-cyclic-Kannan mapping and qpb-cyclic β-quasi-contraction mapping and establish the existence and uniqueness of fixed point theorems for these mappings in quasi-partial b-metric spaces. Some examples are presented to validate our results. c ©2016 All rights reserved.

ARJAN DURRESI,VAMSI PARUCHURI, LEONARD BAROLLI, RAJGOPAL KANNAN, S.S IYENGAR Department of Computer Science, Louisiana State University 298 Coates Hall, Baton Rouge, LA 70803, USA Email:{durresi, paruchuri, rkannan, iyengar}@csc.lsu.edu Department of Information and Communication Engineering Faculty of Information Engineering, Fukuoka Institute of Technology (FIT) 3-30-1 Wajiro-Higashi, Higashi...