This paper discusses the energy efficient QoS topology control problem in ad hoc wireless networks. Given a set of nodes in a plane, end-toend traffic demands and delay bounds between node pairs, the problem is to find a network topology that can meet the QoS requirements and the total transmission power of nodes is minimized. We consider two cases of the problem: 1) the traffic demands are not...

We devise the first polynomial time algorithm computing a pure Nash equilibriumfor atomic splittable congestion games with singleton strategies and player-specificaffine cost functions. Our algorithm is purely combinatorial and computes the exactequilibrium assuming rational input. The idea is to compute a pure Nash equilibriumfor an associated integrally-splittable singleton co...

In this work we study weighted network congestion games with playerspecific latency functions where selfish players wish to route their traffic through a shared network. We consider both the case of splittable and unsplittable traffic. Our main findings are as follows: – For routing games on parallel links with linear latency functions without a constant term we introduce two new potential func...

Password-based authenticated key exchange (PAKE) enables two users with shared low-entropy passwords to establish cryptographically strong session keys over insecure networks. At Asiacrypt 2009, Katz and Vaikuntanathan showed a generic three-round PAKE based on any CCA-secure PKE with associated approximate smooth projective hashing (ASPH), which helps to obtain the first PAKE from lattices. In...

Link homotopy has been an active area of research for knot theorists since its introduction by Milnor in the 1950s. We introduce a new equivalence relation on spatial graphs called component homotopy, which reduces to link homotopy in the classical case. Unlike previous attempts at generalizing link homotopy to spatial graphs, our new relation allows analogues of some standard link homotopy res...

The notion of almost alternating links was introduced by C. Adams et al ([1]). Here we give a sufficient condition for an almost alternating link diagram to represent a non-splittable link. This solves a question asked in [1]. A partial solution for special almost alternating links has been obtained by M. Hirasawa ([4]). As its applications, Theorem 2.3 gives us a way to see if a given almost a...

The concept of balancedly splittable orthogonal designs is introduced along with a recursive construction. As an application, equiangular tight frames over the real, complex, and quaternions meeting Delsarte–Goethals–Seidel upper bound are obtained.

A flat solvmanifold is a compact quotient $$\Gamma \backslash G$$ where G simply-connected solvable Lie group endowed with left invariant metric and $$ lattice of G. Any such can be written as $$G={\mathbb {R}}^k < imes _{\phi } {\mathbb {R}}^m$$ $${\mathbb the nilradical. In this article we focus on 6-dimensional splittable solvmanifolds, which are obtained quotienting by that decomposed =\Gam...