This paper focuses on optimal path planning for vehicles in known environments. Previous work has presented mixed integer linear programming (MILP) formulations, which suffer from scalability issues as the number of obstacles, and hence the number of integer variables, increases. In order to address MILP scalability, a novel three-stage algorithm is presented which first computes a desirable pa...

XQuery expressions can manipulate two kinds of order: document order and sequence order. While the user can impose or observe the order of items within a sequence, the results of path expressions must always be returned in document order. Correctness can be obtained by inserting explicit (and expensive) operations to sort and remove duplicates after each XPath step. However, many such operation...

Context: The extended finite state machine (EFSM) is a modelling approach that has been used to represent a wide range of systems. When testing from an EFSM, it is normal to use a test criterion such as transition coverage. Such test criteria are often expressed in terms of transition paths (TPs) through an EFSM. Despite the popularity of EFSMs, testing from an EFSM is difficult for two main re...

We show that, for a natural notion of quasirandomness in k-uniform hypergraphs, any quasirandom k-uniform hypergraph on n vertices with constant edge density and minimum vertex degree Ω(nk−1) contains a loose Hamilton cycle. We also give a construction to show that a k-uniform hypergraph satisfying these conditions need not contain a Hamilton `-cycle if k − ` divides k. The remaining values of ...

Sequencing activities over time is a fundamental optimization problem. The problem can be modeled using a directed network in which activities are represented by nodes and pairs of activities that can be performed consecutively are represented by arcs. A sequence of activities then corresponds to a path in the directed network, and an optimal sequence of activities, assuming appropriately chose...

In this paper, the current status of chicken genomics is reviewed. This is timely given the current intense activity centred on sequencing the complete genome of this model species. The genome project is based on a decade of map building by genetic linkage and cytogenetic methods, which are now being replaced by high-resolution radiation hybrid and bacterial artificial chromosome (BAC) contig m...

A new algorithm for solving linear complementarity problems with suucient matrices is proposed. If the problem has a solution the algorithm is superlinearly convergent from any positive starting points, even for degenerate problems. Each iteration requires only one matrix factorization and at most two backsolves. Only one backsolve is necessary if the problem is known to be nondegenerate. The a...

An amino acid sequence of a protein may be decomposed into consecutive overlapping strings of length K. How unique is the converse, i.e., reconstruction of amino acid sequences using the set of K-strings obtained in the decomposition? This problem may be transformed into the problem of counting the number of Eulerian loops in an Euler graph, though the well-known formula must be modified. By ex...

In 2000, Babson and Steingŕımsson introduced the notion of what is now known as a permutation vincular pattern, and based on it they re-defined known Mahonian statistics and introduced new ones, proving or conjecturing their Mahonity. These conjectures were proved by Foata and Zeilberger in 2001, and by Foata and Randrianarivony in 2006. In 2010, Burstein refined some of these results by giving...

We study statistics on ordered set partitions whose generating functions are related to p, q-Stirling numbers of the second kind. The main purpose of this paper is to provide bijective proofs of all the conjectures of Steingŕımsson(Arxiv:math.CO/0605670). Our basic idea is to encode ordered partitions by a kind of path diagrams and explore the rich combinatorial properties of the latter structu...