Incremental Medians via Online Bidding

In the k-median problem we are given sets of facilities and customers, and distances between them. For a given set F of facilities, the cost of serving a customer u is the minimum distance between u and a facility in F. The goal is to find a set F of k facilities that minimizes the sum, over all customers, of their service costs. Following Mettu and Plaxton, we study the incremental medians problem, where k is not known in advance, and the algorithm produces a nested sequence of facility sets where the kth set has size k. The algorithm is c-cost-competitive if the cost of each set is at most c times the cost of the optimum set of size k. We give improved incremental algorithms for the metric version: an 8-cost-competitive deterministic algorithm, a 2e ~ 5.44-cost-competitive randomized algorithm, a (24+epsilon)-cost-competitive, poly-time deterministic algorithm, and a (6e+epsilon ~ .31)-cost-competitive, poly-time randomized algorithm. The algorithm is s-size-competitive if the cost of the kth set is at most the minimum cost of any set of size k, and has size at most s k. The optimal size-competitive ratios for this problem are 4 (deterministic) and e (randomized). We present the first poly-time O(log m)-size-approximation algorithm for the offline problem and first poly-time O(log m)-size-competitive algorithm for the incremental problem. Our proofs reduce incremental medians to the following online bidding problem: faced with an unknown threshold T, an algorithm submits "bids" until it submits a bid that is at least the threshold. It pays the sum of all its bids. We prove that folklore algorithms for online bidding are optimally competitive.Comment: conference version appeared in LATIN 2006 as "Oblivious Medians via Online Bidding

Consumerism and Health: Whose Body Is It, Anyway?

(This information was taken from the Distinguished Scientist Lecture Series Program 1984-1985). Dr. Fagin is Dean of the School of Nursing at the University of Pennsylvania. Born in New York City, she received the Ph.D. from New York University. While earning her doctorate, Dr. Fagin taught at New York University, concentrating on psychiatric and mental health nursing. Prior to her appointment as dean at the University of Pennsylvania, she was director of the Health Professions Institute of Herbert H. Lehman College and was associated with the Montefiore Hospital and Medical Center. Dr. Fagin has edited and written a number of books, including Nursing in Child Psychiatry (1972) and Family Centered Nursing in Community Psychiatry (1970), chosen as Books of the Year in their respective areas by The American Journal of Nursing. Her articles have appeared extensively in professional journals and published anthologies on nursing, psychiatry, and nursing administration. Among Dr. Fagin\u27s many awards have been two fellowships from the National Institute for Mental Health, a Special Distinguished Alumnus A ward at the 50th Anniversary of Nursing at New York University, and an Honorary Doctorate of Science degree from Lycoming College in Pennsylvania. She has served on the Executive Committee of the Board of Directors of the American Orthopsychiatric Association, on the Expert Advisory Panel on Nursing World Health Organization, and on the National Institute of Mental Health\u27s SCOPCE Research Panel. She is a member of the American Academy of Nursing and the Institute of Medicine of the National Academy of Science. Her professional and public service activities have also included service on editorial and advisory boards and on the special task force on the Mental Health of Children and the New York State Governor\u27s Committee on Children. Her Work: Dr. Fagin\u27s major area of research has been the affects of maternal attendance during children\u27s hospitalization, and many improvements in practice have been based on her work. Continuing to investigate this area, she is currently doing research on the cost effectiveness of nursing intervention and nurse-consumer collaboration. Her Lecture: April 27, 1985: Consumerism and Health: Whose Body Is It, Anyway?https://digitalcommons.bard.edu/dsls_1984_1985/1003/thumbnail.jp

Reasoning about integrity constraints for tree-structured data

International audienceWe study a class of integrity constraints for tree-structured data modelled as data trees, whose nodes have a label from a finite alphabet and store a data value from an infinite data domain. The constraints require each tuple of nodes selected by a conjunctive query (using navigational axes and labels) to satisfy a positive combination of equalities and a positive combination of inequalities over the stored data values. Such constraints are instances of the general framework of XML-to-relational constraints proposed recently by Niewerth and Schwentick. They cover some common classes of constraints, including W3C XML Schema key and unique constraints, as well as domain restrictions and denial constraints, but cannot express inclusion constraints, such as reference keys. Our main result is that consistency of such integrity constraints with respect to a given schema (modelled as a tree automaton) is decidable. An easy extension gives decidability for the entailment problem. Equivalently, we show that validity and containment of unions of conjunctive queries using navigational axes, labels, data equalities and inequalities is decidable, as long as none of the conjunctive queries uses both equalities and inequalities; without this restriction, both problems are known to be undecidable. In the context of XML data exchange, our result can be used to establish decidability for a consistency problem for XML schema mappings. All the decision procedures are doubly exponential, with matching lower bounds. The complexity may be lowered to singly exponential, when conjunctive queries are replaced by tree patterns, and the number of data comparisons is bounded