The Prize-Collecting Steiner Tree Problem (PCST) on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. PCST appears in the design of utility networks (eg. fiber optics or district heating) where profit generating customers and the network connecting the...

This paper is the second part of a two-part paper which introduces a general schema theory for genetic programming (GP) with subtree-swapping crossover (Part I (Poli and McPhee, 2003)). Like other recent GP schema theory results, the theory gives an exact formulation (rather than a lower bound) for the expected number of instances of a schema at the next generation. The theory is based on a Car...

While price and data quality should define the major tradeoff for consumers in data markets, prices are usually prescribed by vendors and data quality is not negotiable. In this paper we study a model where data quality can be traded for a discount. We focus on the case of XML documents and consider completeness as the quality dimension. In our setting, the data provider offers an XML document,...

We consider a new combinatorial optimization problem that combines network design and facility location aspects. Given a graph with two types of customers and two technologies that can be installed on the edges, the objective is to find a minimum cost subtree connecting all customers while the primary customers are served by a primary subtree that is embedded into the secondary subtree. In addi...

A hypergraph H = (V,E) is a subtree hypergraph if there is a tree T on V such that each hyperedge of E induces a subtree of T . To find a minimum size transversal for a subtree hypergraph is, in general, NP-hard. In this paper, we show that if it is possible to decide if a set of vertices W ⊆ V is a transversal in time S(n) ( where n = |V | ), then it is possible to find a minimum size transver...

In this paper, an m-level optimal subtree based phonetic decision tree clustering algorithm is described. Unlike prior approaches, the m-level optimal subtree in the proposed approach is to generate log likelihood estimates using multiple mixture Gaussians for phonetic decision tree based state tying. It provides a more accurate model of the log likelihood variations in node splitting and it is...

In this paper a new general GP schema theory for headless chicken crossover and subtree mutation is presented. The theory gives an exact formulation for the expected number of instances of a schema at the next generation. The theory includes four main results: microscopic schema theorems for both headless chicken crossover and subtree mutation, and two corresponding macroscopic theorems. The mi...

1. INTERACTIVE BEHAVIOR TREES Interactive Behavior Trees (IBT’s) address challenges in traditional Behavior Tree representations by facilitating freeform user interaction and state persistence. IBT’s, as illustrated in Fig. 1(a) are divided into 3 independent sub-trees that are connected using a Parallel control node. An IBT tIBT = 〈tui, tstate, tnarr = {t i |t 1 . . . t m }, β〉 where: (1) tnar...

The graph-theoretic operation of rooted subtree prune and regraft is increasingly being used as a tool for understanding and modelling reticulation events in evolutionary biology. In this paper, we show that computing the rooted subtree prune and regraft distance between two rooted binary phylogenetic trees on the same label set is NP-hard. This resolves a longstanding open problem. Furthermore...

Network design involves several areas of engineering and science. Computer networks, electrical circuits, transportation problems, and phylogenetic trees are some examples. In general, these problems are NP-Hard. In order to deal with the complexity of these problems, several strategies have been proposed. Among them, approaches using evolutionary algorithms have achieved relevant results. Howe...