The Stable Roommates problem with short lists

We consider two variants of the classical Stable Roommates problem with Incomplete (but strictly ordered) preference lists SRI that are degree constrained, i.e., preference lists are of bounded length. The first variant, EGAL d-SRI, involves finding an egalitarian stable matching in solvable instances of SRI with preference lists of length at most d. We show that this problem is NP-hard even if d=3. On the positive side we give a (2d+3)/7-approximation algorithm for d={3,4,5} which improves on the known bound of 2 for the unbounded preference list case. In the second variant of SRI, called d-SRTI, preference lists can include ties and are of length at most d. We show that the problem of deciding whether an instance of d-SRTI admits a stable matching is NP-complete even if d=3. We also consider the "most stable" version of this problem and prove a strong inapproximability bound for the d=3 case. However for d=2 we show that the latter problem can be solved in polynomial time.Comment: short version appeared at SAGT 201

Guest editorial: Special issue on matching under preferences

No abstract available

Local search for stable marriage problems with ties and incomplete lists

The stable marriage problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools, or more generally to any two-sided market. We consider a useful variation of the stable marriage problem, where the men and women express their preferences using a preference list with ties over a subset of the members of the other sex. Matchings are permitted only with people who appear in these preference lists. In this setting, we study the problem of finding a stable matching that marries as many people as possible. Stability is an envy-free notion: no man and woman who are not married to each other would both prefer each other to their partners or to being single. This problem is NP-hard. We tackle this problem using local search, exploiting properties of the problem to reduce the size of the neighborhood and to make local moves efficiently. Experimental results show that this approach is able to solve large problems, quickly returning stable matchings of large and often optimal size.Comment: 12 pages, Proc. PRICAI 2010 (11th Pacific Rim International Conference on Artificial Intelligence), Byoung-Tak Zhang and Mehmet A. Orgun eds., Springer LNA

Manipulating Tournaments in Cup and Round Robin Competitions

In sports competitions, teams can manipulate the result by, for instance, throwing games. We show that we can decide how to manipulate round robin and cup competitions, two of the most popular types of sporting competitions in polynomial time. In addition, we show that finding the minimal number of games that need to be thrown to manipulate the result can also be determined in polynomial time. Finally, we show that there are several different variations of standard cup competitions where manipulation remains polynomial.Comment: Proceedings of Algorithmic Decision Theory, First International Conference, ADT 2009, Venice, Italy, October 20-23, 200

Coreference detection of low quality objects

The problem of record linkage is a widely studied problem that aims to identify coreferent (i.e. duplicate) data in a structured data source. As indicated by Winkler, a solution to the record linkage problem is only possible if the error rate is sufficiently low. In other words, in order to succesfully deduplicate a database, the objects in the database must be of sufficient quality. However, this assumption is not always feasible. In this paper, it is investigated how merging of low quality objects into one high quality object can improve the process of record linkage. This general idea is illustrated in the context of strings comparison, where strings of low quality (i.e. with a high typographical error rate) are merged into a string of high quality by using an n-dimensional Levenshtein distance matrix and compute the optimal alignment between the dirty strings. Results are presented and possible refinements are proposed

What Affects Social Attention? Social Presence, Eye Contact and Autistic Traits

Social understanding is facilitated by effectively attending to other people and the subtle social cues they generate. In order to more fully appreciate the nature of social attention and what drives people to attend to social aspects of the world, one must investigate the factors that influence social attention. This is especially important when attempting to create models of disordered social attention, e.g. a model of social attention in autism. Here we analysed participants' viewing behaviour during one-to-one social interactions with an experimenter. Interactions were conducted either live or via video (social presence manipulation). The participant was asked and then required to answer questions. Experimenter eye-contact was either direct or averted. Additionally, the influence of participant self-reported autistic traits was also investigated. We found that regardless of whether the interaction was conducted live or via a video, participants frequently looked at the experimenter's face, and they did this more often when being asked a question than when answering. Critical differences in social attention between the live and video interactions were also observed. Modifications of experimenter eye contact influenced participants' eye movements in the live interaction only; and increased autistic traits were associated with less looking at the experimenter for video interactions only. We conclude that analysing patterns of eye-movements in response to strictly controlled video stimuli and natural real-world stimuli furthers the field's understanding of the factors that influence social attention. © 2013 Freeth et al

A Minimal Periods Algorithm with Applications

Kosaraju in ``Computation of squares in a string'' briefly described a linear-time algorithm for computing the minimal squares starting at each position in a word. Using the same construction of suffix trees, we generalize his result and describe in detail how to compute in O(k|w|)-time the minimal k-th power, with period of length larger than s, starting at each position in a word w for arbitrary exponent $k\geq2$ and integer $s\geq0$. We provide the complete proof of correctness of the algorithm, which is somehow not completely clear in Kosaraju's original paper. The algorithm can be used as a sub-routine to detect certain types of pseudo-patterns in words, which is our original intention to study the generalization.Comment: 14 page

Rapid Accurate Calculation of the s-Wave Scattering Length

Transformation of the conventional radial Schr\"odinger equation defined on the interval $\,r\in[0,\infty)$ into an equivalent form defined on the finite domain $\,y(r)\in [a,b]\,$ allows the s-wave scattering length $a_s$ to be exactly expressed in terms of a logarithmic derivative of the transformed wave function $\phi(y)$ at the outer boundary point $y=b$, which corresponds to $r=\infty$. In particular, for an arbitrary interaction potential that dies off as fast as $1/r^n$ for $n\geq 4$, the modified wave function $\phi(y)$ obtained by using the two-parameter mapping function $r(y;\bar{r},\beta) = \bar{r}[1+\frac{1}{\beta}\tan(\pi y/2)]$ has no singularities, and $$a_s=\bar{r}[1+\frac{2}{\pi\beta}\frac{1}{\phi(1)}\frac{d\phi(1)}{dy}].$$ For a well bound potential with equilibrium distance $r_e$, the optimal mapping parameters are $\,\bar{r}\approx r_e\,$ and $\,\beta\approx \frac{n}{2}-1$. An outward integration procedure based on Johnson's log-derivative algorithm [B.R.\ Johnson, J.\ Comp.\ Phys., \textbf{13}, 445 (1973)] combined with a Richardson extrapolation procedure is shown to readily yield high precision $a_s$-values both for model Lennard-Jones ($2n,n$) potentials and for realistic published potentials for the Xe--e$^-$, Cs_2(a\,^3\Sigma_u^+) and $^{3,4}$He_2(X\,^1\Sigma_g^+) systems. Use of this same transformed Schr{\"o}dinger equation was previously shown [V.V. Meshkov et al., Phys.\ Rev.\ A, {\bf 78}, 052510 (2008)] to ensure the efficient calculation of all bound levels supported by a potential, including those lying extremely close to dissociation.Comment: 12 pages, 9 figures, to appear in J. Chem. Phy

Wiretapping a hidden network

We consider the problem of maximizing the probability of hitting a strategically chosen hidden virtual network by placing a wiretap on a single link of a communication network. This can be seen as a two-player win-lose (zero-sum) game that we call the wiretap game. The value of this game is the greatest probability that the wiretapper can secure for hitting the virtual network. The value is shown to equal the reciprocal of the strength of the underlying graph. We efficiently compute a unique partition of the edges of the graph, called the prime-partition, and find the set of pure strategies of the hider that are best responses against every maxmin strategy of the wiretapper. Using these special pure strategies of the hider, which we call omni-connected-spanning-subgraphs, we define a partial order on the elements of the prime-partition. From the partial order, we obtain a linear number of simple two-variable inequalities that define the maxmin-polytope, and a characterization of its extreme points. Our definition of the partial order allows us to find all equilibrium strategies of the wiretapper that minimize the number of pure best responses of the hider. Among these strategies, we efficiently compute the unique strategy that maximizes the least punishment that the hider incurs for playing a pure strategy that is not a best response. Finally, we show that this unique strategy is the nucleolus of the recently studied simple cooperative spanning connectivity game

Hierarchies of Predominantly Connected Communities

We consider communities whose vertices are predominantly connected, i.e., the vertices in each community are stronger connected to other community members of the same community than to vertices outside the community. Flake et al. introduced a hierarchical clustering algorithm that finds such predominantly connected communities of different coarseness depending on an input parameter. We present a simple and efficient method for constructing a clustering hierarchy according to Flake et al. that supersedes the necessity of choosing feasible parameter values and guarantees the completeness of the resulting hierarchy, i.e., the hierarchy contains all clusterings that can be constructed by the original algorithm for any parameter value. However, predominantly connected communities are not organized in a single hierarchy. Thus, we develop a framework that, after precomputing at most $2(n-1)$ maximum flows, admits a linear time construction of a clustering \C(S) of predominantly connected communities that contains a given community $S$ and is maximum in the sense that any further clustering of predominantly connected communities that also contains $S$ is hierarchically nested in \C(S). We further generalize this construction yielding a clustering with similar properties for $k$ given communities in $O(kn)$ time. This admits the analysis of a network's structure with respect to various communities in different hierarchies.Comment: to appear (WADS 2013