Improved Output-Sensitive Snap Rounding

An intersection-sensitive algorithm for snap rounding

Snap rounding is a method for converting arbitrary-precision arrangements of segments into fixed-precision representation. We present an algorithm for snap rounding with running time O((n + I) log n), where I is the number of intersections between the input segments. In the worst case, our algorithm is an order of magnitude more efficient than the best previously known algorithms. We also propo...

Iterated snap rounding

Extending the Power of Snap Rounding Variants

Snap Rounding (SR for short) is a method for converting arbitrary-precision arrangements of line segments into a fixed-precision representation. In the previous years two variants of SR were presented: Iterated Snap Rounding (ISR) and Iterated Snap Rounding with Bounded Drift (ISRBD). Their goal was to eliminate an undesirable property that SR possesses. Prior to their appearances, the capabili...

Efficient Snap Rounding with Integer Arithmetic

In this paper we present a slightly modified definition of snap rounding, and provide two efficient algorithms that perform this rounding. The first algorithm takes n line segments as input and generates the set of snapped segments in O(|I| + Σc is(c) log n + |I∗ m|), where |I| is the complexity of the unrounded arrangement I, is(c) is the number of segments that have an intersection or endpoin...

Improved output-sensitive quantum algorithms for Boolean matrix multiplication

We present new quantum algorithms for Boolean Matrix Multiplication in both the time complexity and the query complexity settings. As far as time complexity is concerned, our results show that the product of two n× n Boolean matrices can be computed on a quantum computer in time Õ(n3/2+nl3/4), where l is the number of non-zero entries in the product, improving over the outputsensitive quantum a...