We study the Capacitated k-Median problem for which existing constant-factor approximation algorithms are all pseudo-approximations that violate either the capacities or the upper bound k on the number of open facilities. Using the natural LP relaxation for the problem, one can only hope to get the violation factor down to 2. Li [SODA’16] introduced a novel LP to go beyond the limit of 2 and ga...

OBJECTIVE Diet soda consumption increases cardiometabolic risk. The aim of this investigation was to assess the relations between self-reported soda consumption and subclinical cardiac remodeling. METHODS We assessed the relations between self-reported soda consumption and left ventricular mass (LVM) and left atrial dimension (LAD) (both standardized within sex) in a sample of middle-aged att...

OBJECTIVE To determine if baking soda toothpastes are relatively more effective than non-baking soda toothpastes in promoting plaque removal from less accessible sites in the dentition. METHODS Several single-brushing comparisons of baking soda and non-baking soda toothpastes for their overall ability to remove plaque have been published. In this study, individual comparisons of these publish...

The present study examines the direct effects of television commercials advertising soda on actual sugar-sweetened soda consumption among young women. An experimental-observational study design was used, in which 51 female students (ages 18-29) were exposed to a 35-min movie clip, interrupted by two commercial breaks consisting of soda or water commercials. Their actual soda consumption while w...

We study the Capacitated k-Median problem for which existing constant-factor approximation algorithms are all pseudo-approximations that violate either the capacities or the upper bound k on the number of open facilities. Using the natural LP relaxation for the problem, one can only hope to get the violation factor down to 2. Li [SODA’16] introduced a novel LP to go beyond the limit of 2 and ga...

We develop a new lower bound technique for data structures. We show an optimal Ω(n lg lgn/ lgn) space lower bounds for storing an index that allows to implement rank and select queries on a bit vector B provided that B is stored explicitly. These results improve upon [Miltersen, SODA’05]. We show Ω((m/t) lg t) lower bounds for storing rank/select index in the case where B has m 1-bits in it (e....

To examine whether artificial sweeteners aid in the control of long-term food intake and body weight, we gave free-living, normal-weight subjects 1150 g soda sweetened with aspartame (APM) or high-fructose corn syrup (HFCS) per day. Relative to when no soda was given, drinking APM-sweetened soda for 3 wk significantly reduced calorie intake of both females (n = 9) and males (n = 21) and decreas...

Let s be a string whose symbols are solely available through access(i), a read-only operation that probes s and returns the symbol at position i in s. Many compressed data structures for strings, trees, and graphs, require two kinds of queries on s: select(c, j), returning the position in s containing the jth occurrence of c, and rank(c, p), counting how many occurrences of c are found in the f...

OBJECTIVE An earlier clinical study demonstrated that brushing with a commercial Arm & Hammer dentifrice containing baking soda physically removed significantly more plaque than brushing with either of two commercial dentifrices which did not contain baking soda. However, little has been done to confirm these results and to compare baking soda-containing dentifrices with more recently commercia...

We study low-rank approximation in the streaming model in which the rows of an n × d matrix A are presented one at a time in an arbitrary order. At the end of the stream, the streaming algorithm should output a k × d matrix R so that ‖A−ARR‖F ≤ (1 + )‖A−Ak‖F , where Ak is the best rank-k approximation to A. A deterministic streaming algorithm of Liberty (KDD, 2013), with an improved analysis of...