A lower bound is presented which shows that a class of heap algorithms in the pointer model with only heap pointers must spend Ω ( log log n log log log n ) amortized time on the Decrease-Key operation (given O(logn) amortized-time Extract-Min). Intuitively, this bound shows the key to having O(1)-time Decrease-Key is the ability to sort O(log n) items in O(log n) time; Fibonacci heaps [M. .L. ...

water by the latter alone, although it is known to manufacturers that sweet drinks require much less carbon dioxide than soda-water. The chief complaint about their soda-water was that it did not hold as much carbon dioxide in solution as some of the best soda-waters placed on the market by other manufacturers. The company employs the latest method of manufacture. Carbon dioxide is generated by...

In their seminal paper [Sleator and Tarjan, J.ACM, 1985], the authors conjectured that the splay tree is dynamically optimal binary search tree (BST). In spite of decades of intensive research, the problem remains open. Perhaps a more basic question, which has also attracted much attention, is if there exists any dynamically optimal BST algorithm. One such candidate is GREEDY which is a simple ...

We investigate labeling schemes supporting adjacency, ancestry, sibling, and connectivity queries in forests. In the course of more than 20 years, the existence of logn + O(log log) labeling schemes supporting each of these functions was proven, with the most recent being ancestry [Fraigniaud and Korman, STOC ’10]. Several multi-functional labeling schemes also enjoy lower or upper bounds of lo...

Diospyrobezoars are a subtype of phytobezoars caused by excessive consumption of persimmons, which contain large amounts of tannins. In contrast to phytobezoars, diospyrobezoars have a harder consistency than other bezoars, making them more difficult to break up both chemically and endoscopically. We have previously reported successful dissolution of phytobezoars with diet soda and cellulase. A...

We assessed public opinion on nutrition-related policies to address child obesity: a soda tax, restrictions on advertising unhealthy foods and beverages to children, and restrictions on siting fast food restaurants and convenience stores near schools. We analyzed data from 998 adults (aged ≥18 years) in the 2011 Los Angeles County Health Survey. Support was highest for advertising restrictions ...

Haloalkaliphiles are double extremophilic organisms thriving both at high salinity and alkaline pH. Although numerous haloalkaliphilic representatives have been identified among Archaea and Bacteria over the past 15 years, the adaptations underlying their prosperity at haloalkaline conditions are scarcely known. A multi-level adaptive strategy was proposed to occur in haloalkaliphilic organisms...

I have heard that the main reason why diet drinks, like a diet soda, can be bad on a diet, is that it can spike insulin levels and then your body expects sugar that it does not get. I have taken to the habit of only occasionally having diet drinks with meals, so that any increase in insulin is actually met with food in my system. My question is whether or not this is a good/workable strategy, o...

The string matching problem on a node-labeled graph $$G=(V,E)$$ asks whether given pattern P has an occurrence in G, the form of path whose concatenation node labels equals P. This is basic primitive various problems bioinformatics, databases, or networks, but only recently proven to have O(|E||P|)-time lower bound, under Orthogonal Vectors Hypothesis (OVH). We consider here its indexed version...

The problem of (? +1)-vertex coloring a graph maximum degree ? has been extremely well studied over the years in various settings and models. Surprisingly, for dynamic setting, almost nothing was known until recently. In SODA’18, Bhattacharya, Chakrabarty, Henzinger Nanongkai devised randomized algorithm maintaining +1)-coloring with O (log ?) expected amortized update time. this article, we pr...