Online knowledge libraries refer to the online data warehouses that systematically organize and categorize the knowledge-based information about different kinds of concepts and entities. In the era of big data, the setup of online knowledge libraries is an extremely challenging and laborious task, in terms of efforts, time and expense required in the completion of knowledge entities. Especially nowadays, a large number of new knowledge entities, like movies, are keeping on being produced and coming out at a continuously accelerating speed, which renders the knowledge library setup and completion problem more difficult to resolve manually. In this paper, we will take the online movie knowledge libraries as an example, and study the "Multiple aligned ISomeric Online Knowledge LIbraries Completion problem" (Miso-Klic) problem across multiple online knowledge libraries. Miso-Klic aims at identifying the missing entities for multiple knowledge libraries synergistically and ranking them for editing based on certain ranking criteria. To solve the problem, a thorough investigation of two isomeric online knowledge libraries, Douban and IMDB, have been carried out in this paper. Based on analyses results, a novel deep online knowledge library completion framework "Integrated Deep alignEd Auto-encoder" (IDEA) is introduced to solve the problem. By projecting the entities from multiple isomeric knowledge libraries to a shared feature space, IDEA solves the Miso-Klic problem via three steps: (1) entity feature space unification via embedding, (2) knowledge library fusion based missing entity identification, and (3) missing entity ranking. Extensive experiments done on the real-world online knowledge library dataset have demonstrated the effectiveness of IDEA in addressing the problem.
 This book probes the stable marriage problem and its variants as a rich source of problems and ideas that illustrate both the design and analysis of efficient algorithms. It covers the most recent structural and algorithmic work on stable matching problems, simplifies and unifies many earlier proofs, strengthens several earlier results, and presents new results and more efficient algorithms.The authors develop the structure of the set of stable matchings in the stable marriage problem in a more general and algebraic context than has been done previously; they discuss the problem's structure in terms of rings of sets, which allows many of the most useful features to be seen as features of a more general set of problems. The relationship between the structure of the stable marriage problem and the more general stable roommates problem is demonstrated, revealing many commonalities.The results the authors obtain provide an algorithmic response to the practical, and political, problems created by the asymmetry inherent in the Gale Shapley solutions, leading to alternative methods and better compromises than are provided by the Gale Shapley method. And, in contrast to Donald Knuth's earlier work which primarily focused on the application of mathematics to the analysis of algorithms, this book illustrates the productive and almost inseparable relationship between mathematical insight and the design of efficient algorithms.Dan Gusfield is Associate Professor of Computer Science at the University of California, Davis. Robert W. Irving is Senior Lecturer in Computing Science at the University of Glasgow. The Stable Marriage Problem is included in the Foundations of Computing Series, edited by Michael Garey and Albert Meyer.  Both rematching proof and strong equilibrium outcomes are stable with respect to the true preferences in the marriage problem. We show that not all rematching proof or strong equilibrium outcomes are stable in the college admissions problem. But we show that both rematching proof and strong equilibrium outcomes in truncations at the match point are all stable in the college admissions problem. Further, all true stable matchings can be achieved in both rematching proof and strong equilibrium in truncations at the match point. We show that any Nash equilibrium in truncations admits one and only one matching, stable or not. Therefore, the core at a Nash equilibrium in truncations must be small. But examples exist such that the set of stable matchings with respect to a Nash equilibrium may contain more than one matching. Nevertheless, each Nash equilibrium can only admit at most one true stable matching. If, indeed, there is a true stable matching at a Nash equilibrium, then the only possible equilibrium outcome will be the true stable matching, no matter how different are players' equilibrium strategies from the true preferences and how many other unstable matchings are there at that Nash equilibrium. Thus, we show that a necessary and sufficient condition for the stable matching rule to be implemented in a subset of Nash equilibria by the direct revelation game induced by a stable mechanism is that every Nash equilibrium profile in that subset admits one and only one true stable matching. We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose–accept rounds executed by the Gale–Shapley algorithm for the stable marriage problem. Consequently, the participants can arrive at an almost stable matching even without full information about the problem instance; for each participant, knowing only its local neighbourhood is enough. In distributed-systems parlance, this means that if each person has only a constant number of acceptable partners, an almost stable matching emerges after a constant number of synchronous communication rounds. We apply our results to give a distributed (2+e)-approximation algorithm for maximum-weight matching in bicoloured graphs and a centralised randomised constant-time approximation scheme for estimating the size of a stable matching. Online social networks can often be represented as heterogeneous information networks containing abundant information about: who, where, when and what. Nowadays, people are usually involved in multiple social networks simultaneously. The multiple accounts of the same user in different networks are mostly isolated from each other without any connection between them. Discovering the correspondence of these accounts across multiple social networks is a crucial prerequisite for many interesting inter-network applications, such as link recommendation and community analysis using information from multiple networks. In this paper, we study the problem of anchor link prediction across multiple heterogeneous social networks, i.e., discovering the correspondence among different accounts of the same user. Unlike most prior work on link prediction and network alignment, we assume that the anchor links are one-to-one relationships (i.e., no two edges share a common endpoint) between the accounts in two social networks, and a small number of anchor links are known beforehand. We propose to extract heterogeneous features from multiple heterogeneous networks for anchor link prediction, including user's social, spatial, temporal and text information. Then we formulate the inference problem for anchor links as a stable matching problem between the two sets of user accounts in two different networks. An effective solution, MNA (Multi-Network Anchoring), is derived to infer anchor links w.r.t. the one-to-one constraint. Extensive experiments on two real-world heterogeneous social networks show that our MNA model consistently outperform other commonly-used baselines on anchor link prediction. Users' locations are important for many applications such as personalized search and localized content delivery. In this paper, we study the problem of profiling Twitter users' locations with their following network and tweets. We propose a multiple location profiling model (MLP), which has three key features: 1) it formally models how likely a user follows another user given their locations and how likely a user tweets a venue given his location, 2) it fundamentally captures that a user has multiple locations and his following relationships and tweeted venues can be related to any of his locations, and some of them are even noisy, and 3) it novelly utilizes the home locations of some users as partial supervision. As a result, MLP not only discovers users' locations accurately and completely, but also "explains" each following relationship by revealing users' true locations in the relationship. Experiments on a large-scale data set demonstrate those advantages. Particularly, 1) for predicting users' home locations, MLP successfully places 62 users and out-performs two state-of-the-art methods by 10 in accuracy, 2) for discovering users' multiple locations, MLP improves the baseline methods by 14 in recall, and 3) for explaining following relationships, MLP achieves 57 accuracy. A stable matching rule is used as the outcome function for the Admission game where colleges behave straightforwardly and the students’ strategies are given by their preferences over the colleges. We show that the college-optimal stable matching rule implements the set of stable matchings via the Nash equilibrium (NE) concept. For any other stable matching rule the strategic behavior of the students may lead to outcomes that are not stable under the true preferences. We then introduce uncertainty about the matching selected and prove that the natural solution concept is that of NE in the strong sense. A general result shows that the random stable matching rule, as well as any stable matching rule, implements the set of stable matchings via NE in the strong sense. Precise answers are given to the strategic questions raised. Abstract Two-sided matching markets of the kind known as the “college admissions problem” have been widely thought to be virtually equivalent to the simpler “marriage problem” for which some striking results concerning agents' preferences and incentives have been recently obtained. It is shown here that some of these results do not generalize to the college admissions problem, contrary to a number of assertions in the recent literature. No stable matching procedure exists that makes it a dominant strategy for colleges to reveal their true preferences, and some outcomes may be preferred by all colleges to the college-optimal stable outcome.