Mobile ad hoc network (MANET) is a set of wireless mobile computer forming a temporary network with out any wired infrastructure, due to dynamic nature of topology and other constraints transmission routing is a challenging task in MANET. k path splittable routing establish at most k paths between single source and single destination node, this scheme provides better load balancing and increase...

We study the convex hull of the splittable flow arc set with capacity and minimum load constraints. This set arises as a relaxation of problems where clients have demand for a resource that can be installed in integer amounts and that has capacity limitations and lower bounds on utilization. We prove that the convex hull of this set is the intersection of the convex hull of the set with a capac...

We provide some new conditions under which the graded Betti numbers of a mono-mial ideal can be computed in terms of the graded Betti numbers of smaller ideals, thus complementing Eliahou and Kervaire's splitting approach. As applications, we show that edge ideals of graphs are splittable, and we provide an iterative method for computing the Betti numbers of the cover ideals of Cohen-Macaulay b...

We study the problem of selfishly routing splittable traffic with respect to maximum congestion through a shared network. Our model naturally combines features of the two best studied models in the context of selfish routing: The KP-model [11] and the Wardrop-model [20]. We are given a network with source nodes si, sink nodes ti, 1 ≤ i ≤ k, m edges, and a latency function for each edge. Traffic...

Fog computing networks have been widely integrated in IoT-based systems to improve the quality of services (QoS) such as low response service delay through efficient offloading algorithms. However, designing an solution is still facing many challenges including complicated heterogeneity fog devices and complex computation tasks. In addition, need for a scalable distributed algorithm with comput...

Cooperative communications has long been proposed as an effective method for reducing the energy consumption of the mobile terminals (MTs) in wireless cellular networks. However, it is hard to be implemented due to the lack of incentives for the MTs to cooperate. In this paper, we propose a pricing mechanism to incentivize the uplink cooperative communications for the energy saving of MTs. We f...

In classical network flow theory, flow being sent from a source to a destination may be split into a large number of chunks traveling on different paths through the network. This effect is undesired or even forbidden in many applications. Kleinberg introduced the unsplittable flow problem where all flow traveling from a source to a destination must be sent on only one path. This is a generaliza...