Erik Demaine Scribe : Siddhartha Sen 1

Lower Bounds : Fun With Hardness Proofs Fall 2014 Lecture 11 Scribe Notes

Recall that one of the most commonly used reductions is the L-reduction, introduced by Papadim­ itriou and Yannakakis in [?]. This reduction consists of a pair of polynomial mappings (f(.), g(.)) where f maps an instance x of the problem A we are reducing from to an instance x/ of the problem B we are reducing to, and g maps a feasible solution y/ (of x/ i.e. instance of B) to a feasible soluti...

Algorithmic Lower Bounds : Fun With Hardness Proofs Fall 2014 Lecture 3 Scribe Notes

Last time, we established the hardness of two fundamental problems, (2-)Partition and 3-Partition, and exhibited a bunch of reductions from those problems to other numerical and geometrical ones. Today, we continue with reductions from 3and 2-Partition to geometrical problems—we’ll also use the fact that the problem of packing n squares into a square without rotations is strongly NP-complete, a...

Erik Demaine Scribe : Eric Price 1 Overview

• Comparison sort: O(n lg n) • Counting sort: O(n + u) = O(n + 2w) (= O(n) for w = lg n) • Radix sort: O(n · w lg n) (= O(n) for w = O(lg n)) • van Emde Boas: O(n lg w). For w = lg n, this is O(n lg lg n). This can be improved to O(n lg w lg n), making it better than the previous methods (Kirkpatrick and Reisch [7]). • Signature sort: O(n) for w = Ω(lg n). Combined with the previous result for ...

Êê Blockin Blockinòø Êê×ùðø× Ò Óñôùøøøøóòòð Çööööññ

Narrow Misère Dots-and-Boxes

We study misère Dots-and-Boxes, where the goal is to minimize score, for narrow boards. In particular, we characterize the winner for 1× n boards with an explicit winning strategy for the first player with a score of b(n − 1)/3c. We also give preliminary results for 2 × n and for Swedish 1× n (where the boundary is initially drawn).