It is well known that every 2-edge-connected graph can be oriented so that the resulting digraph is strongly connected. Here we study the problem of orienting a connected graph with cut edges in order to maximize the number of ordered vertex pairs (x, y) such that there is a directed path from x to y. After transforming this problem, we prove a key theorem about the transformed problem that allows us to obtain a quadratic algorithm for the original orientation problem. We also consider how to orient graphs to minimize the number of ordered vertex pairs joined by a directed path. After showing this problem is equivalent to the comparability graph completion problem, we show both problems are NP-hard, and even NP-hard to approximate to within a factor of 1 + ε, for some ε > 0. © 1997 Published by Elsevier Science B.V.

Intense few-cycle laser pulses have a breadth of applications in high energy density science, including particle acceleration and x-ray generation. Multi-amplifier laser system pulses have durations of tens of femtoseconds or longer. To achieve high intensities at the single-cycle limit, a robust and efficient post-compression scheme is required. We demonstrate a staged compression technique using self-phase modulation in thin dielectric media, in which few-cycle pulses can be produced. The few-cycle pulse is then used to generate extreme ultravoilet light via high harmonic generation at strong field intensities and to generate MeV electron beams via laser solid interactions at relativistic intensities.

There is urgent need to develop new acceleration techniques capable of exceeding gigaelectron-volt-per-metre (GeV m(-1)) gradients in order to enable future generations of both light sources and high-energy physics experiments. To address this need, short wavelength accelerators based on wakefields, where an intense relativistic electron beam radiates the demanded fields directly into the accelerator structure or medium, are currently under intense investigation. One such wakefield based accelerator, the dielectric wakefield accelerator, uses a dielectric lined-waveguide to support a wakefield used for acceleration. Here we show gradients of 1.347±0.020 GeV m(-1) using a dielectric wakefield accelerator of 15 cm length, with sub-millimetre transverse aperture, by measuring changes of the kinetic state of relativistic electron beams. We follow this measurement by demonstrating accelerating gradients of 320±17 MeV m(-1). Both measurements improve on previous measurements by and order of magnitude and show promise for dielectric wakefield accelerators as sources of high-energy electrons.