We show that the K1,1,3-free partial 2-trees and the Halin graphs other than K4 can all be represented as proper contact graphs of squares in the plane. Among partial 2-trees and Halin graphs, these are exactly the ones that can be embedded without nonempty triangles, which form an obstacle to the existence of square contact representations. However the graph of a square antiprism has no such representation despite being embeddable without any nonempty triangles.
We experiment with sorting algorithms in the evolving data model, in which, at the same time as the algorithm compares pairs of elements and possibly chooses a new ordering based on the results of the comparison, an adversary randomly chooses two adjacent elements in the sorted order and swaps them. As we show, bubble sort and its variants appear to maintain an order that is within inversion distance of optimal.
Co-authors – Publications – David Eppstein – Theory Group – Inf. & Comp. Sci. – UC Irvine
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