A Stable Marriage Requires Communication

The Gale-Shapley algorithm for the Stable Marriage Problem is known to take $\Theta(n^2)$ steps to find a stable marriage in the worst case, but only $\Theta(n \log n)$ steps in the average case (with $n$ women and $n$ men). In 1976, Knuth asked whether the worst-case running time can be improved in a model of computation that does not require sequential access to the whole input. A partial negative answer was given by Ng and Hirschberg, who showed that $\Theta(n^2)$ queries are required in a model that allows certain natural random-access queries to the participants' preferences. A significantly more general - albeit slightly weaker - lower bound follows from Segal's general analysis of communication complexity, namely that $\Omega(n^2)$ Boolean queries are required in order to find a stable marriage, regardless of the set of allowed Boolean queries. Using a reduction to the communication complexity of the disjointness problem, we give a far simpler, yet significantly more powerful argument showing that $\Omega(n^2)$ Boolean queries of any type are indeed required for finding a stable - or even an approximately stable - marriage. Notably, unlike Segal's lower bound, our lower bound generalizes also to (A) randomized algorithms, (B) allowing arbitrary separate preprocessing of the women's preferences profile and of the men's preferences profile, (C) several variants of the basic problem, such as whether a given pair is married in every/some stable marriage, and (D) determining whether a proposed marriage is stable or far from stable. In order to analyze "approximately stable" marriages, we introduce the notion of "distance to stability" and provide an efficient algorithm for its computation

Visual Representations of Gender and Computing in Consumer and Professional Magazines

Studies in the nineteen-eighties showed that advertising images of computers were gendered, with women relatively less represented, and shown with less empowered roles, problems or presented as sexual objects. This paper uses a mix of content and interpretative analysis to analyse current imagery in consumerist and professional society publications. It reveals the present variation and complexity of the iconography of computers and people across different domains of representation, with the continuation of gender bias in subtle forms

The women in IT (WINIT) final report

The Women in IT (WINIT) project was funded by the European Social Fund (ESF) from March 2004 until April 2006 under HE ESF Objective 3: Research into equal opportunities in the labour market. Specifically the project came under Policy Field 2, Measure 2: Gender discrimination in employment. The project was run in the Information Systems Institute of the University of Salford. One of the Research Associates has an information systems (IS) background, the other has a background in sociology. We begin this report with an overview of the current situation with regards women in the UK IT sector. Whilst gender is only recently being recognised as an issue within the mainstream IS academic community, thirty years of female under-representation in the ICT field in more general terms has received more attention from academics, industry and government agencies alike. Numerous research projects and centres (such as the UK Resource Centre for Women in Science, Engineering and Technology) exist to tackle the under-representation of women in SET careers, although the figures for women’s participation in the ICT sector remain disheartening, with current estimates standing at around 15% (EOC 2004). Various innovative initiatives, such as e-Skills’ Computer Clubs for Girls, appear to have had little impact on these low female participation rates. Additionally, these and other initiatives have been interpreted as a means to fill the skills gap and ‘make up the numbers’ to boost the UK economy (French and Richardson 2005), resulting in ‘add more women and stir’ solutions to the ‘problem’ of gender in relation to inclusion in IS and ICT (Henwood 1996). Given that there have been decades of equal opportunity and related policies as well as many government initiatives designed to address the gender imbalance in IT employment patterns, sex segregation in IT occupations and pay and progression disparity in the IT sector (including the latest initiative- a one million pound DTI funded gender and SET project), we could be forgiven for assuming that these initiatives have had a beneficial effect on the position and number of women in the IT workforce, and that even if we have not yet achieved gender equity, we can surely argue that there are positive moves in the right direction. Although we do not wish to make definitive claims about the success or failure of specific initiatives, our research, backed up by recent major surveys, paints a picture that remains far from rosy. Indeed a recent comparative survey of the IT workforce in Germany, Holland and the UK indicates that women are haemorrhaging out of the UK IT workforce (Platman and Taylor 2004). From a high point of 100,892 women in the UK IT workforce in 1999, Platman and Taylor (ibid., 8) report a drop to 53,759 by 2003. As the IT industry was moving into recession anyway, the number of men in the industry has also declined, but by nothing like as much, so the figures for women are stark. When it comes to number crunching who is employed in the UK IT sector and when trying to make historical comparisons, the first obstacle is defining the sector itself. Studies vary quite substantially in the number of IT workers quoted suggesting there is quite a bit of variation in what is taken to be an IT job. The IT industry has experienced considerable expansion over the past twenty years. In spring 2003 in Britain, it was estimated that almost 900,000 people worked in ICT firms, and there were over 1 million ICT workers, filling ICT roles in any sector (e-Skills UK, 2003). This growth has resulted in talk of a ‘skills shortage’ requiring the ‘maximization’ of the workforce to its full potential: ‘You don’t just need pale, male, stale guys in the boardroom but a diversity of views’ (Stone 2004). In spring 2003 the Equal Opportunities Commission estimated there to be 151,000 women working in ICT occupations compared with 834,000 men (clearly using a different, much wider job definition from that of Platman and Taylor (2004)) , whilst in the childcare sector, there were less than 10,000 men working in these occupations, compared with 297,000 women (EOC 2004). It is estimated that the overall proportion of women working in ICT occupations is 15% (EOC 2004). In the UK, Office of National Statistics (ONS) statistics indicate that women accounted for 30% of IT operations technicians, but a mere 15% of ICT Managers and only 11% of IT strategy and planning professionals (EOC 2004). Although women are making inroads into technical and senior professions there remains a ‘feminisation’ of lower level jobs, with a female majority in operator and clerical roles and a female minority in technical and managerial roles (APC 2004).

Solving stable matching problems using answer set programming

Since the introduction of the stable marriage problem (SMP) by Gale and Shapley (1962), several variants and extensions have been investigated. While this variety is useful to widen the application potential, each variant requires a new algorithm for finding the stable matchings. To address this issue, we propose an encoding of the SMP using answer set programming (ASP), which can straightforwardly be adapted and extended to suit the needs of specific applications. The use of ASP also means that we can take advantage of highly efficient off-the-shelf solvers. To illustrate the flexibility of our approach, we show how our ASP encoding naturally allows us to select optimal stable matchings, i.e. matchings that are optimal according to some user-specified criterion. To the best of our knowledge, our encoding offers the first exact implementation to find sex-equal, minimum regret, egalitarian or maximum cardinality stable matchings for SMP instances in which individuals may designate unacceptable partners and ties between preferences are allowed. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).Comment: Under consideration in Theory and Practice of Logic Programming (TPLP). arXiv admin note: substantial text overlap with arXiv:1302.725

Production of pace as collaborative activity

In this paper we investigate the concept of pace development and management among groups of people. We explore and compare groups visiting museums, and groups virtually co-located in a mixed reality system for a museum. In considering pace, and how to design to support it, we have to consider more than the speed or location of information display. We have to also take into consideration the social formation of pace through features such as the visitors' awareness of each other's location and attention. By considering aspects of collaboratively produced pace such as presenting engagement and disengagement, we offer suggestions as to how social handling of pace might be better supported by technology

The Complexity of Approximately Counting Stable Matchings

We investigate the complexity of approximately counting stable matchings in the $k$-attribute model, where the preference lists are determined by dot products of "preference vectors" with "attribute vectors", or by Euclidean distances between "preference points" and "attribute points". Irving and Leather proved that counting the number of stable matchings in the general case is #P-complete. Counting the number of stable matchings is reducible to counting the number of downsets in a (related) partial order and is interreducible, in an approximation-preserving sense, to a class of problems that includes counting the number of independent sets in a bipartite graph (#BIS). It is conjectured that no FPRAS exists for this class of problems. We show this approximation-preserving interreducibilty remains even in the restricted $k$-attribute setting when $k \geq 3$ (dot products) or $k \geq 2$ (Euclidean distances). Finally, we show it is easy to count the number of stable matchings in the 1-attribute dot-product setting.Comment: Fixed typos, small revisions for clarification, et