How Hard Is It to Satisfy (Almost) All Roommates?

The classic Stable Roommates problem (the non-bipartite generalization of the well-known Stable Marriage problem) asks whether there is a stable matching for a given set of agents, i.e. a partitioning of the agents into disjoint pairs such that no two agents induce a blocking pair. Herein, each agent has a preference list denoting who it prefers to have as a partner, and two agents are blocking if they prefer to be with each other rather than with their assigned partners. Since stable matchings may not be unique, we study an NP-hard optimization variant of Stable Roommates, called Egal Stable Roommates, which seeks to find a stable matching with a minimum egalitarian cost gamma, i.e. the sum of the dissatisfaction of the agents is minimum. The dissatisfaction of an agent is the number of agents that this agent prefers over its partner if it is matched; otherwise it is the length of its preference list. We also study almost stable matchings, called Min-Block-Pair Stable Roommates, which seeks to find a matching with a minimum number beta of blocking pairs. Our main result is that Egal Stable Roommates parameterized by gamma is fixed-parameter tractable, while Min-Block-Pair Stable Roommates parameterized by beta is W[1]-hard, even if the length of each preference list is at most five

Proceedings of the 2022 XCSP3 Competition

This document represents the proceedings of the 2022 XCSP3 Competition. The results of this competition of constraint solvers were presented at FLOC (Federated Logic Conference) 2022 Olympic Games, held in Haifa, Israel from 31th July 2022 to 7th August, 2022.Comment: arXiv admin note: text overlap with arXiv:1901.0183

Pairwise Kidney Exchange

The theoretical literature on exchange of indivisible goods finds natural application in organizing the exchange of live donor kidneys for transplant. However, in kidney exchange, there are constraints on the size of feasible exchanges. Initially, kidney exchanges are likely to be pairwise exchanges, between just two patient-donor pairs, as these are logistically simpler than larger exchanges. Furthermore, the experience of many American surgeons suggests to them that preferences over kidneys are approximately 0-1, i.e. that patients and surgeons should be largely indifferent among healthy donors whose kidneys are compatible with the patient. This is because, in the United States, transplants of compatible live kidneys have about equal graft survival probabilities, regardless of the closeness of tissue types between patient and donor. We show that, although the pairwise constraint eliminates some potential exchanges, there is a wide class of constrained-efficient mechanisms that are strategy-proof when patient-donor pairs and surgeons have 0-1 preferences. This class of mechanisms includes deterministic mechanisms that would accomodate the kinds of priority setting that organ banks currently use to allocate cadaver organs, as well as stochastic mechanisms that allow distributive justice issues to be

Pairwise Kidney Exchange

In connection with an earlier paper on the exchange of live donor kidneys (Roth, S”nmez, and šnver 2004) the authors entered into discussions with New England transplant surgeons and their colleagues in the transplant community, aimed at implementing a Kidney Exchange program. In the course of those discussions it became clear that a likely first step will be to implement pairwise exchanges, between just two patient-donor pairs, as these are logistically simpler than exchanges involving more than two pairs. Furthermore, the experience of these surgeons suggests to them that patient and surgeon preferences over kidneys should be 0-1, i.e. that patients and surgeons should be indifferent among kidneys from healthy donors whose kidneys are compatible with the patient. This is because, in the United States, transplants of compatible live kidneys have about equal graft survival `robabilities, regardless of the closeness of tissue types between patient and dOnor (unless there is a rare perfect match). In the present paper we show that, although thd pairwise constraint eliminates some potential exchanges, there is a wide class of constrained-efficient mechanisms 4hat are strategy-proof when patient-donor pairs and surgeons have 0-1 preferences. This class of meahanisms includes deterministic mechanisms that would accomodate the kinds of priority setting that organ banks currently use for the allocation of cadaver organs, as well as stochastic mechanisms that allow considerations of distributive justice to be addressed.

Interior point methods and simulated annealing for nonsymmetric conic optimization

This thesis explores four methods for convex optimization. The first two are an interior point method and a simulated annealing algorithm that share a theoretical foundation. This connection is due to the interior point method’s use of the so-called entropic barrier, whose derivatives can be approximated through sampling. Here, the sampling will be carried out with a technique known as hit-and-run. By carefully analyzing the properties of hit-and-run sampling, it is shown that both the interior point method and the simulated annealing algorithm can solve a convex optimization problem in the membership oracle setting. The number of oracle calls made by these methods is bounded by a polynomial in the input size. The third method is an analytic center cutting plane method that shows promising performance for copositive optimization. It outperforms the first two methods by a significant margin on the problem of separating a matrix from the completely positive cone. The final method is based on Mosek’s algorithm for nonsymmetric conic optimization. With their scaling matrix, search direction, and neighborhood, we define a method that converges to a near-optimal solution in polynomial time

Machine learning on Web documents

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (leaves 111-115).The Web is a tremendous source of information: so tremendous that it becomes difficult for human beings to select meaningful information without support. We discuss tools that help people deal with web information, by, for example, blocking advertisements, recommending interesting news, and automatically sorting and compiling documents. We adapt and create machine learning algorithms for use with the Web's distinctive structures: large-scale, noisy, varied data with potentially rich, human-oriented features. We adapt two standard classification algorithms, the slow but powerful support vector machine and the fast but inaccurate Naive Bayes, to make them more effective for the Web. The support vector machine, which cannot currently handle the large amount of Web data potentially available, is sped up by "bundling" the classifier inputs to reduce the input size. The Naive Bayes classifier is improved through a series of three techniques aimed at fixing some of the severe, inaccurate assumptions Naive Bayes makes. Classification can also be improved by exploiting the Web's rich, human-oriented structure, including the visual layout of links on a page and the URL of a document. These "tree-shaped features" are placed in a Bayesian mutation model and learning is accomplished with a fast, online learning algorithm for the model. These new methods are applied to a personalized news recommendation tool, "the Daily You." The results of a 176 person user-study of news preferences indicate that the new Web-centric techniques out-perform classifiers that use traditional text algorithms and features. We also show that our methods produce an automated ad-blocker that performs as well as a hand-coded commercial ad-blocker.by Lawrence Kai Shih.Ph.D

Co-Design of Time-Invariant Dynamical Systems

Design of a physical system and its controller has significant ramifications on the overall system performance. The traditional approach of first optimizing the physical design and then the controller may lead to sub-optimal solutions. This is due to the interdependence between the physical design and control parameters through the dynamic equations. Recognition of this fact paved the way for investigation into the ``Co-Design" research theme wherein the overall system's physical design and control are simultaneously optimized. Co-design involves simultaneous optimization of the design and the control variables with respect to certain structural property as constraint. The structural property may be in the form of stability, observability or controllability leading to different types of co-design problems. Co-design optimization problems are non-convex optimization problems involving bilinear matrix inequality (BMI) constraints and are NP-hard in general. In this dissertation, four interrelated research tasks in the area of co-design are undertaken. In the first research task, a theoretical and computational framework is developed to co-design a class of linear time invariant (LTI) dynamical systems. A novel solution procedure based on an iterative combination of generalized Benders decomposition and gradient projection method is developed guaranteeing convergence to a solution in a finite number of iterations which is within a tolerance bound from the nearest local/global minimum. In the second research task, the sparse and structured static feedback design problem is modeled as a co-design problem. A formulation based on the alternating direction method of multipliers is used to solve the sparse feedback design problem which has given robustness as a constraint. In the third research task, the optimal actuator placement problem is formulated as a co-design problem. The actuator positions are modeled as $0/1-$binary design variables and result in a mixed integer nonlinear programming (MINLP) problem. In the fourth research task, a heuristic procedure to place sensors and design observer is developed for a class of Lipschitz nonlinear systems. The procedure is based on the relation between Lipschitz constant, sensor locations and observer gain. The vast and diverse application potential of co-design across all engineering branches is the primary motivation and relevance of the research work carried out in this dissertation