Algorithms for Highly Symmetric Linear and Integer Programs

This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of lower dimension. Combining this approach with knowledge of the geometry of feasible integer solutions yields an algorithm for solving highly symmetric integer linear programs which only takes time which is linear in the number of constraints and quadratic in the dimension.Comment: 21 pages, 1 figure; some references and further comments added, title slightly change

Extended formulations from communication protocols in output-efficient time

Deterministic protocols are well-known tools to obtain extended formulations, with many applications to polytopes arising in combinatorial optimization. Although constructive, those tools are not output-efficient, since the time needed to produce the extended formulation also depends on the number of rows of the slack matrix (hence, on the exact description in the original space). We give general sufficient conditions under which those tools can be implemented as to be output-efficient, showing applications to e.g.~Yannakakis' extended formulation for the stable set polytope of perfect graphs, for which, to the best of our knowledge, an efficient construction was previously not known. For specific classes of polytopes, we give also a direct, efficient construction of extended formulations arising from protocols. Finally, we deal with extended formulations coming from unambiguous non-deterministic protocols

Realizability of Polytopes as a Low Rank Matrix Completion Problem

This article gives necessary and sufficient conditions for a relation to be the containment relation between the facets and vertices of a polytope. Also given here, are a set of matrices parameterizing the linear moduli space and another set parameterizing the projective moduli space of a combinatorial polytope

Quantum Computing with NMR

A review of progress in NMR quantum computing and a brief survey of the literatureComment: Commissioned by Progress in NMR Spectroscopy (95 pages, no figures

Towards Minimal Barcodes

In the setting of persistent homology computation, a useful tool is the persistence barcode representation in which pairs of birth and death times of homology classes are encoded in the form of intervals. Starting from a polyhedral complex K (an object subdivided into cells which are polytopes) and an initial order of the set of vertices, we are concerned with the general problem of searching for filters (an order of the rest of the cells) that provide a minimal barcode representation in the sense of having minimal number of “k-significant” intervals, which correspond to homology classes with life-times longer than a fixed number k. As a first step, in this paper we provide an algorithm for computing such a filter for k = 1 on the Hasse diagram of the poset of faces of K

On a Clique-Based Integer Programming Formulation of Vertex Colouring with Applications in Course Timetabling

Vertex colouring is a well-known problem in combinatorial optimisation, whose alternative integer programming formulations have recently attracted considerable attention. This paper briefly surveys seven known formulations of vertex colouring and introduces a formulation of vertex colouring using a suitable clique partition of the graph. This formulation is applicable in timetabling applications, where such a clique partition of the conflict graph is given implicitly. In contrast with some alternatives, the presented formulation can also be easily extended to accommodate complex performance indicators (``soft constraints'') imposed in a number of real-life course timetabling applications. Its performance depends on the quality of the clique partition, but encouraging empirical results for the Udine Course Timetabling problem are reported

a direct encoding for nnc polyhedra

We present an alternative Double Description representation for the domain of NNC (not necessarily closed) polyhedra, together with the corresponding Chernikova-like conversion procedure. The representation uses no slack variable at all and provides a solution to a few technical issues caused by the encoding of an NNC polyhedron as a closed polyhedron in a higher dimension space. A preliminary experimental evaluation shows that the new conversion algorithm is able to achieve significant efficiency improvements

Historical influence on the practice of chiropractic radiology: part II - thematic analysis on the opinions of diplomates of the American Chiropractic College of Radiology about the future

Background: Over the past 20 years, various authors have addressed the question of the future of chiropractic. Most were positive about the future, with some advocating evidence-based practice and integration with mainstream healthcare, some advocating continued separation with an emphasis on subluxation-based care or the traditional/historical paradigm of chiropractic, and some calling for tolerance and unity. No papers were found specifically inquiring about the future of chiropractic radiology. Methods: The study population consisted of all current members of the American Chiropractic College of Radiology (ACCR), estimated at 190 people, known as chiropractic radiologists or Diplomates of the American Chiropractic Board of Radiology (DACBRs). An internet-based, anonymous survey using SurveyMonkey was implemented, supplemented by hard copies distributed at a conference. The main point of interest for this paper is the final item of the overall questionnaire. This item inquired about the future of chiropractic radiology. Thematic analysis was used on the responses, coded in both constructionist and inductive ways to extract both a general outlook and more specific themes. The inductive themes were also assigned secondarily to a SWOT (strengths, weaknesses, opportunities, and threats) analysis. Results: The overall response rate to the survey was 38% (73/190); within the group of respondents, 71 of 73 (98%) answered the item that is the subject of this paper. Opinions on the outlook for chiropractic radiology in the future were more negative than positive, with 14 respondents giving a positive outlook, 26 negative, and 14 non-committal. 28 respondents advocated integration with the wider healthcare community, 11 recommended emphasising separateness or a focus on working within chiropractic, and 15 did not express an opinion on this issue. Ten strengths were noted, 11 weaknesses, 57 opportunities, and 30 threats. Conclusions: The increasing necessity of demonstrating evidence for diagnostic and therapeutic procedures in healthcare makes it likely that chiropractic radiologists and the wider chiropractic profession will need to take a more active position on evidence-based practice. Re-evaluation of guidelines and legislation as well as enforcement policies and practices will be necessary. The consequences of failing to do so may include increased marginalisation and reduced viability as a profession

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject