We consider the popular matching problem in a roommates instance G = (V,E) with strict preference lists. While popular matchings always exist in a bipartite instance, they need not exist in a roommates instance. The complexity of the popular matching problem in a roommates instance has been an open problem for several years and here we show it is NP-hard. A sub-class of max-size popular matchin...

We study dynamic matching problems in graphs among agents with preferences. Agents and/or edges of the graph arrive and depart iteratively over time. The goal is to maintain matchings that are favorable to the agent population and stable over time. More formally, we strive to keep a small unpopularity factor by making only a small amortized number of changes to the matching per round. Our main ...

Figurative Note. Abstract images are constructed by an algorithm that randomly assigns elements to adesign. Painted figurative images conform to complexity level in corresponding VDT Abstract.Both VDT Abstract and Figurative images were co-calibrated to define a common artistic judg-ment aptitude construct.PERSONS MAP OF ITEMS| +|. |||...

We provide further explanation of the significance of an example in a recent paper of Wolf in the context of the problem of finding large subspaces in sumsets. Throughout these notes G will denote the group F2 , that is the n-dimensional vector space over F2, and PG will denote the normalized counting measure on G. The convolution of two functions f, g ∈ L(PG) is defined to be f ∗ g(x) := ∫

Agricultural biotechnology, especially genetic engineering or genetic modification (GM), is a topic of considerable controversy worldwide. The public debate is fraught with polarized views and opinions, some are held with religious zeal. Unfortunately, it is also marked with much ignorance and misinformation. Here we explore some popular misconceptions encountered in the public debate.

In an instance G = (A∪B,E) of the stable marriage problem with strict and possibly incomplete preference lists, a matchingM is popular if there is no matchingM ′ where the vertices that prefer M ′ to M outnumber those that prefer M to M ′. All stable matchings are popular and there is a simple linear time algorithm to compute a maximum-size popular matching. More generally, what we seek is a mi...

For a set A of n applicants and a set I of m items, let us consider the problem of matching applicants to items, where each applicant x ∈ A provides its preference list defined on items. We say that an applicant x prefers an item p than an item q if p is located at higher position than q in its preference list. For any matchingsM andM′ of the matching problem, we say that an applicant x prefers...