On Online Labeling with Polynomially Many Labels

In the online labeling problem with parameters n and m we are presented with a sequence of n keys from a totally ordered universe U and must assign each arriving key a label from the label set {1,2,...,m} so that the order of labels (strictly) respects the ordering on U. As new keys arrive it may be necessary to change the labels of some items; such changes may be done at any time at unit cost for each change. The goal is to minimize the total cost. An alternative formulation of this problem is the file maintenance problem, in which the items, instead of being labeled, are maintained in sorted order in an array of length m, and we pay unit cost for moving an item. For the case m=cn for constant c>1, there are known algorithms that use at most O(n log(n)^2) relabelings in total [Itai, Konheim, Rodeh, 1981], and it was shown recently that this is asymptotically optimal [Bul\'anek, Kouck\'y, Saks, 2012]. For the case of m={\Theta}(n^C) for C>1, algorithms are known that use O(n log n) relabelings. A matching lower bound was claimed in [Dietz, Seiferas, Zhang, 2004]. That proof involved two distinct steps: a lower bound for a problem they call prefix bucketing and a reduction from prefix bucketing to online labeling. The reduction seems to be incorrect, leaving a (seemingly significant) gap in the proof. In this paper we close the gap by presenting a correct reduction to prefix bucketing. Furthermore we give a simplified and improved analysis of the prefix bucketing lower bound. This improvement allows us to extend the lower bounds for online labeling to the case where the number m of labels is superpolynomial in n. In particular, for superpolynomial m we get an asymptotically optimal lower bound {\Omega}((n log n) / (log log m - log log n)).Comment: 15 pages, Presented at European Symposium on Algorithms 201

Weighted ancestors in suffix trees

The classical, ubiquitous, predecessor problem is to construct a data structure for a set of integers that supports fast predecessor queries. Its generalization to weighted trees, a.k.a. the weighted ancestor problem, has been extensively explored and successfully reduced to the predecessor problem. It is known that any solution for both problems with an input set from a polynomially bounded universe that preprocesses a weighted tree in O(n polylog(n)) space requires \Omega(loglogn) query time. Perhaps the most important and frequent application of the weighted ancestors problem is for suffix trees. It has been a long-standing open question whether the weighted ancestors problem has better bounds for suffix trees. We answer this question positively: we show that a suffix tree built for a text w[1..n] can be preprocessed using O(n) extra space, so that queries can be answered in O(1) time. Thus we improve the running times of several applications. Our improvement is based on a number of data structure tools and a periodicity-based insight into the combinatorial structure of a suffix tree.Comment: 27 pages, LNCS format. A condensed version will appear in ESA 201

Quantum dots coordinated with conjugated organic ligands: new nanomaterials with novel photophysics

CdSe quantum dots functionalized with oligo-(phenylene vinylene) (OPV) ligands (CdSe-OPV nanostructures) represent a new class of composite nanomaterials with significantly modified photophysics relative to bulk blends or isolated components. Single-molecule spectroscopy on these species have revealed novel photophysics such as enhanced energy transfer, spectral stability, and strongly modified excited state lifetimes and blinking statistics. Here, we review the role of ligands in quantum dot applications and summarize some of our recent efforts probing energy and charge transfer in hybrid CdSe-OPV composite nanostructures

Changes in invertebrate assemblage composition in benthic and hyporheic zones during a severe supraseasonal drought

Droughts are unpredictable disturbances characterized in streams by declining flow, reduced habitat availability, and deteriorating abiotic conditions. Such events typically reduce benthic invertebrate taxon richness and modify assemblage composition, but little is known about how hyporheic invertebrate assemblages respond to drought or how these responses relate to changes in benthic assemblages. We hypothesized that taxon richness (diversity) and variability (as within-site diversity) in benthic assemblage composition would decline as drought proceeded, whereas concurrent changes in hyporheic assemblages would be lower in this more stable environment. We predicted that benthic assemblage composition between sites would converge as epigean taxa were selectively eliminated, whereas between-site hyporheic diversity would change little. We sampled benthic and hyporheic invertebrates concurrently from 4 sites along a groundwater-fed stream during the final stages of a severe supraseasonal drought punctuated by a record heat wave. Abiotic conditions in benthic habitats deteriorated as flow declined, but changes were less pronounced in the hyporheic zone. Benthic diversity declined during drought, whereas hyporheic diversity changed little. However, benthic within-site diversity increased as the drought progressed because of localized variation in the abundance of common taxa. Temporal trends in hyporheic diversity were less consistent. Benthic assemblages at individual sites became more similar, especially during the heat wave, reflecting low diversity and abundance. Hyporheic assemblages changed markedly because of temporary increases in abundances of epigean and hypogean amphipods. These contrasting responses of benthic and hyporheic assemblages to drought should be recognized when developing management strategies for drought-impacted streams