The Largest Empty Circle problem seeks the largest circle centered within the convex hull of a set P of n points in R2 and devoid of points from P . In this paper, we introduce a query version of this well-studied problem. In our query version, we are required to preprocess P so that when given a query line Q, we can quickly compute the largest empty circle centered at some point on Q and withi...

Amaximal independent set is an independent set that is not a proper subset of any other independent set. Jou and Chang determined the largest number of maximal independent sets among all graphs and connected graphs of order n, which contain at most one cycle. Later B. E. Sagan and V. R. Vatter found the largest number of maximal independent sets among all graphs of order n, which contain at mos...

Let Q = {qj, qz,..., qn / be a set of n points on the plane. The largest empty circle (LEC) problem consists in finding the largest circle C with center in the convex hull of Q such that no point q(C Q lies in the interior of C. Shamos recently outlined an O(n log n) algorithm for solving this problemJ 9) In this paper it is shown that this algorithm does not always work correctly. A different ...

Given a set of blue points and a set of red points in ddimensional space, we show how to find an axis-aligned hyperrectangle that contains no red points and as many blue points as possible. Our algorithm enumerates the set of relevant hyperrectangles (inclusion maximal axisaligned hyperrectangles that do not contain a red point) and counts the number of blue points in each one. The runtime of o...

A well-known conjecture of Thomassen states that every cycle of maximum order in a 3-connected graph contains a chord. While many partial results towards this conjecture have been obtained, the conjecture itself remains unsolved. In this paper, we prove a stronger result without a connectivity assumption for graphs of high minimum degree, which shows Thomassen’s conjecture holds in that case. T...

BACKGROUND The respiratory cycle alters the size of the right internal jugular vein (RIJV). We assessed the changes in RIJV size during the respiratory cycle in patients under positive pressure ventilation. Moreover, we examined the effects of positive-end expiratory pressure (PEEP) and the Trendelenburg position on respiratory fluctuations. METHODS A prospective study of 24 patients undergoi...

We find an explicit bound, in terms of g when it is even, for the largest element of an aliquot cycle of repdigits to base g.

in this paper, the effects of input temperature and compression ratio on the net output work and efficiency of the air standard cycles, i.e. atkinson cycle, diesel cycle and otto cycle are analyzed. we assumed that the compression and power processes are adiabatic and reversible and any convective, conductive and radiative heat transfer to cylinder wall during the heat rejection process may be ...