Let F be a field and Gr(i, F ) be the Grassmannian of idimensional linear subspaces of F . A map f : Gr(i, F ) −→ Gr(j, F ) is called nesting if l ⊂ f(l) for every l ∈ Gr(i, F ). Glover, Homer and Stong showed that there are no continuous nesting maps Gr(i, C) −→ Gr(j, C) except for a few obvious ones. We prove a similar result for algebraic nesting maps Gr(i, F ) −→ Gr(j, F ), where F is an al...

Diva J. Amon*, Daniel Sykes, Farah Ahmed, Jonathan T. Copley, Kirsty M. Kemp, Paul A. Tyler, Craig M. Young and Adrian G. Glover 1 Life Sciences Department, Natural History Museum, London, UK 2 Ocean and Earth Science, National Oceanography Centre, Southampton, University of Southampton, Southampton, UK 3 Department of Oceanography, University of Hawai’i at Manoa, Honolulu, HI, USA 4 Imaging an...

To identify the current state-of-the-art, and to better understand the heuristic components that prove most effective for several classes of heuristic algorithms applied to the TSP, the 8th DIMACS Implementation Challenge on the Traveling Salesman Problem [3] was recently organized by Johnson, McGeogh, Glover and Rego [3]. In this talk we describe findings from this Implementation Challenge as ...

Parks have long been sites for sexual activity, deviant behaviour, violence, and prostitution (Flowers, Hart, & Marriot, 1999; Humphreys, 1970; Mitchell, 1995). Yet leisure researchers have tended to leave these less socially acceptable activities unexamined, focusing their analyses instead on the “benefits” of leisure (Glover, 2003; Rojek, 1999, 2000). This research aims to deviate from the “b...

We present the two-loop helicity amplitudes for the scattering of two gluons into two gluons in QCD, which are relevant for next-to-next-to-leading order corrections to jet production at hadron colliders. We give the results in the ‘t Hooft-Veltman and four-dimensional helicity variants of dimensional regularization. Summing our expressions over helicities and colors, and converting to conventi...

We use the notion of domination ratio introduced by Glover and Punnen in 1997 to present a new classification of combinatorial optimization (CO) problems: DOM-easy and DOM-hard problems. It follows from results proved already in the 1970’s that min TSP (both symmetric and asymmetric versions) is DOM-easy. We prove that several CO problems are DOM-easy including weighted max k-SAT and max cut. W...

We present a linearization strategy for mixed 0-1 quadratic programs that produces small formulations with tight relaxations. It combines constructs from a classical method of Glover and a more recent reformulation-linearization technique (RLT). By using binary identities to rewrite the objective, a variant of the first method results in a concise formulation with the level-1 RLT strength. This...

Glover and Punnen (1997) asked whether there exists a polynomial time algorithm that always produces a tour which is not worse than at least n!=p(n) tours for some polynomial p(n) for every TSP instance on n cities. They conjectured that, unless P=NP, the answer to this question is negative. We prove that the answer to this question is, in fact, positive. A generalization of the TSP, the quadra...

The Feasibility Pump of Fischetti, Glover, Lodi, and Bertacco [8, 7] has proved to be a very successful heuristic for finding feasible solutions of mixed integer programs. The quality of the solutions in terms of the objective value, however, tends to be poor. This paper proposes a slight modification of the algorithm in order to find better solutions. Extensive computational results show the s...