One of the key ideas in randomized algorithms is that good outcomes are likely enough to happen if we flip coins. This allows us to avoid distinguishing many cases and treating each separately. In this lecture, we will study one particular such technique, which allows us to design approximation algorithms. In all of our algorithms, we will rely on linear programs (LPs). The examples are selecte...

We consider flow rounding: finding an integral flow from a fractional flow. Costed flow rounding asks that we find an integral flow with no worse cost. Randomized flow rounding requires we randomly find an integral flow such that the expected flow along each edge matches the fractional flow. Both problems are reduced to cycle canceling, for which we develop an O(m log n 2 m ) algorithm.

The following paradigm is often used for handling NP-hard combinatorial optimization problems. One first formulates the problem as an integer program, then one relaxes it to a linear program (LP, or more generally, a convex program), then one solves the LP relaxation in polynomial time, and finally one rounds the optimal LP solution, obtaining a feasible solution to the original problem. Many o...

Recently, sensor databases have been used for many applications such as environment observations or weather forecasting. To construct sensor databases, some researches focus on the rounding sink approach. In the approach, rounding sinks repeatedly round in the area that sensors are deployed and collect data from each sensor. Compared with the traditional wireless sensor network approach, the ro...

Rounding is the familiar practice of reporting one value whenever a real number lies in an interval. Uncertainty about the extent of rounding is common when researchers analyze survey responses to numerical questions. The prevalent practice has been to take numerical responses at face value, even though many may in fact be rounded. This paper studies the rounding of responses to survey question...

BACKGROUND With limited work hours, efficient rounding and effective hand-offs have become essential. We created a completely electronic medical record (EMR)-generated rounding report for use during pre-rounding, team rounds, and sign-out/hand-offs. We hypothesized that this would reduce workloads. METHODS We used a pre- and post-implementation survey of the residents and faculty members of t...

Recently, sensor databases have been used for many applications such as environment observations or weather forecasting. To construct sensor databases, some researches focus on the rounding sink approach. In the approach, rounding sinks repeatedly round in the area that sensors are deployed and collect data from each sensor. Compared with the traditional wireless sensor network approach, the ro...