We study the integer maximum flow problem on wireless sensor networks with energy constraint. In this problem, sensor nodes gather data and then relay them to a base station, before they run out of battery power. Packets are considered as integral units and not splittable. The problem is to find the maximum data flow in the sensor network subject to the energy constraint of the sensors. We show...

the network design problem (ndp) is one of the important problems in combinatorial optimization. among the network design problems, the multicommodity capacitated network design (mcnd) problem has numerous applications in transportation, logistics, telecommunication, and production systems. the mcnd problems with splittable flow variables are np-hard, which means they require exponential time t...

Let Zn be the finite cyclic group of order n and S ⊆ Zn. We examine the factorization properties of the Block Monoid B(Zn, S) when S is constructed using a method inspired by a 1990 paper of Erdős and Zaks. For such a set S, we develop an algorithm in Section 2 to produce and order a set {Mi} i=1 which contains all the non-primary irreducible Blocks (or atoms) of B(Zn, S). This construction yie...

Abstract Kirkman triple systems (KTSs) are among the most popular combinatorial designs and their existence has been settled a long time ago. Yet, in comparison with Steiner systems, little is known about automorphism groups. In particular, there no congruence class representing orders of KTS number automorphisms at least close to points. We partially fill this gap by proving that whenever $$v ...

With more and more businesses and organizations outsourcing their IT services to distributed clouds for cost savings, historical and operational data generated by the services have been growing exponentially. The generated data that are referred to as big data, stored at different geographic datacenters, now become an invaluable asset to these businesses and organizations, as they can make use ...

We study a class of finite strategic games with the property that every deviation of a coalition of players that is profitable to each of its members strictly decreases the lexicographical order of a certain function defined on the set of strategy profiles. We call this property the lexicographical improvement property (LIP) and show that, in finite games, it is equivalent to the existence of a...

Crane and Frenkel proposed a notion of a Hopf category [2]. It was motivated by Lusztig’s approach to quantum groups – his theory of canonical bases. In particular, Lusztig obtains braided deformations Uqn+ of universal enveloping algebras Un+ for some nilpotent Lie algebras n+ together with canonical bases of these braided Hopf algebras [4, 5, 6]. The elements of the canonical basis are identi...

This paper investigates the incentive mechanismdesign from a novel and practically important perspective inwhich mobile users as contributors do not join simultaneouslyand a requester desires large efforts from early contributors.A two-stage Tullock contest framework is constructed: at thesecond stage the potential contributors compete for splittablereward by exerting ef...

Crane and Frenkel proposed a notion of a Hopf category [2]. It was motivated by Lusztig’s approach to quantum groups – his theory of canonical bases. In particular, Lusztig obtains braided deformations Uqn+ of universal enveloping algebras Un+ for some nilpotent Lie algebras n+ together with canonical bases of these braided Hopf algebras [4, 5, 6]. The elements of the canonical basis are identi...

In this thesis we demonstrate the algorithmic usefulness of the so-called Mal’cev correspondence for computations with infinite polycyclic groups. This correspondence between Q-powered nilpotent groups and rational nilpotent Lie algebras was discovered by Anatoly Mal’cev in 1951. We show how the Mal’cev correspondence can be realized on a computer. We explore two possibilities for this purpose ...