Parameterized complexity of the MINCCA problem on graphs of bounded decomposability

In an edge-colored graph, the cost incurred at a vertex on a path when two incident edges with different colors are traversed is called reload or changeover cost. The "Minimum Changeover Cost Arborescence" (MINCCA) problem consists in finding an arborescence with a given root vertex such that the total changeover cost of the internal vertices is minimized. It has been recently proved by G\"oz\"upek et al. [TCS 2016] that the problem is FPT when parameterized by the treewidth and the maximum degree of the input graph. In this article we present the following results for the MINCCA problem: - the problem is W[1]-hard parameterized by the treedepth of the input graph, even on graphs of average degree at most 8. In particular, it is W[1]-hard parameterized by the treewidth of the input graph, which answers the main open problem of G\"oz\"upek et al. [TCS 2016]; - it is W[1]-hard on multigraphs parameterized by the tree-cutwidth of the input multigraph; - it is FPT parameterized by the star tree-cutwidth of the input graph, which is a slightly restricted version of tree-cutwidth. This result strictly generalizes the FPT result given in G\"oz\"upek et al. [TCS 2016]; - it remains NP-hard on planar graphs even when restricted to instances with at most 6 colors and 0/1 symmetric costs, or when restricted to instances with at most 8 colors, maximum degree bounded by 4, and 0/1 symmetric costs.Comment: 25 pages, 11 figure

An analysis on decentralized adaptive MAC protocols for Cognitive Radio networks

The scarcity of bandwidth in the radio spectrum has become more vital since the demand for more and more wireless applications has increased. Most of the spectrum bands have been allocated although many studies have shown that these bands are significantly underutilized most of the time. The problem of unavailability of spectrum and inefficiency in its utilization has been smartly addressed by the Cognitive Radio (CR) Technology which is an opportunistic network that senses the environment, observes the network changes, and then using knowledge gained from the prior interaction with the network, makes intelligent decisions by dynamically adapting their transmission characteristics. In this paper some of the decentralized adaptive MAC protocols for CR networks have been critically analyzed and a novel adaptive MAC protocol for CR networks, DNG-MAC which is decentralized and non-global in nature, has been proposed. The results show the DNG-MAC out performs other CR MAC protocols in terms of time and energy efficiency