Data Structures and Algorithms

2401 Submissions

[2] viXra:2401.0124 [pdf] submitted on 2024-01-24 12:42:56

Timetree: A New Way for Representing Time

Authors: Hui Wang
Comments: 12 Pages.

We always use timeline to describe time, but timeline unable to describe dynamic time. Because dynamic time is on changing, so timeline must be changing too, but it is impossible. Timeline includes layers, relationships existed between layers. If we changed a layer, the others need to be fixed too. Timeline can not make it up automatically, human being must take the work, therefore real-time-changing becomes impossible. It is no matter for film making, but internet needs instant responding, timeline can not cover it. Here we show a new structure called timetree, it is an auto-balanced hierarch structure. Its structure always be complete during changing without help from human being. It is a challenge for making dynamic interactive contents on internet, timetree is born for it. We have tried timeline before now it is the turn of timetree.
Category: Data Structures and Algorithms

[1] viXra:2401.0063 [pdf] submitted on 2024-01-13 21:00:28

The Curve of Matrix Multiplication Schemes

Authors: Warren D. Smith
Comments: 17 Pages.

Various methods have been devised to multiply N×N matrices using O(NE) arithmetic operations when N→∞, for various exponents E with 2<E≤3.However, in practice, the schemes with least known E are not the best, because they only start to win for infeasibly large N. Prior literature has unhealthily been fixated on E alone, i.e. on the asymptotic large-N performance alone. To address that, we propose investigating, for each method, not merely its E, but also its "breakeven N," meaning the least N causing that method to use fewer than the obvious algorithm's N3 bilinear multiplications [or fewer than Strassen'sO(N2.807355) scheme]. The set of (E,logN) datapoints then form a subset of the infinite rectangle (2,3]×[0,∞). Part of that rectangle is filled with datapoints, while another part contains none. What is of interest is the curve delineating the boundary between those two regions.
Category: Data Structures and Algorithms