A quadratic kernel for computing the hybridization number of multiple trees

It has recently been shown that the NP-hard problem of calculating the minimum number of hybridization events that is needed to explain a set of rooted binary phylogenetic trees by means of a hybridization network is fixed-parameter tractable if an instance of the problem consists of precisely two such trees. In this paper, we show that this problem remains fixed-parameter tractable for an arbitrarily large set of rooted binary phylogenetic trees. In particular, we present a quadratic kernel

Treewidth of display graphs: bounds, brambles and applications

Phylogenetic trees and networks are leaf-labelled graphs used to model evolution. Display graphs are created by identifying common leaf labels in two or more phylogenetic trees or networks. The treewidth of such graphs is bounded as a function of many common dissimilarity measures between phylogenetic trees and this has been leveraged in fixed parameter tractability results. Here we further elucidate the properties of display graphs and their interaction with treewidth. We show that it is NP-hard to recognize display graphs, but that display graphs of bounded treewidth can be recognized in linear time. Next we show that if a phylogenetic network displays (i.e. topologically embeds) a phylogenetic tree, the treewidth of their display graph is bounded by a function of the treewidth of the original network (and also by various other parameters). In fact, using a bramble argument we show that this treewidth bound is sharp up to an additive term of 1. We leverage this bound to give an FPT algorithm, parameterized by treewidth, for determining whether a network displays a tree, which is an intensively-studied problem in the field. We conclude with a discussion on the future use of display graphs and treewidth in phylogenetics

RFID Technology in Intelligent Tracking Systems in Construction Waste Logistics Using Optimisation Techniques

Construction waste disposal is an urgent issue for protecting our environment. This paper proposes a waste management system and illustrates the work process using plasterboard waste as an example, which creates a hazardous gas when land filled with household waste, and for which the recycling rate is less than 10% in the UK. The proposed system integrates RFID technology, Rule-Based Reasoning, Ant Colony optimization and knowledge technology for auditing and tracking plasterboard waste, guiding the operation staff, arranging vehicles, schedule planning, and also provides evidence to verify its disposal. It h relies on RFID equipment for collecting logistical data and uses digital imaging equipment to give further evidence; the reasoning core in the third layer is responsible for generating schedules and route plans and guidance, and the last layer delivers the result to inform users. The paper firstly introduces the current plasterboard disposal situation and addresses the logistical problem that is now the main barrier to a higher recycling rate, followed by discussion of the proposed system in terms of both system level structure and process structure. And finally, an example scenario will be given to illustrate the system’s utilization