Big O Theory ClubThoughts on theoretical computer science and research life.
https://theoryclub.github.io/
Mon, 15 Apr 2019 21:40:02 +0000Mon, 15 Apr 2019 21:40:02 +0000Jekyll v3.7.4TSP Approximation Algorithms and Linear Program Basics<p>This meeting is in preparation for the TSP lecture series ARC will be holding from April 23rd to April 25th.</p>
<p>Here are some recommended topics and papers to cover:</p>
<ol>
<li>Symmetric TSP: The 3/2 Approximation by Christofides. https://en.wikipedia.org/wiki/Christofides_algorithm</li>
<li>Asymmetric TSP: The log n Approximation by by Frieze Gabliati and Maffioli.</li>
<li>Symmetric and Asymmetric TSP: Held-Karp LP relaxation.</li>
<li>(Advanced): Uncrossing and laminarity for LPs. https://www.cc.gatech.edu/~vempala/papers/tsp.ps</li>
</ol>
<p>The following paper https://arxiv.org/pdf/1104.3090.pdf was written by the ARC speaker (Ola Svensson) and Tobias Momke has some good overview of previous results as well as some new interesting techniques. These resources should help you utilize the ARC Colloq mini course to the fullest!</p>
Mon, 15 Apr 2019 04:00:00 +0000
https://theoryclub.github.io/2019/tsp
https://theoryclub.github.io/2019/tspblogElections<p>We’ll be electing new officers and talking about future</p>
Mon, 08 Apr 2019 04:00:00 +0000
https://theoryclub.github.io/2019/elections
https://theoryclub.github.io/2019/electionsblogRandomized Algorithms Problem Session<p>Today, we had donuts and a randomized algorithms problem session! This was based of Dr. Vigoda’s CS 6550 class.
We went over Karger’s algorithm, median of means, and more.</p>
Mon, 01 Apr 2019 04:00:00 +0000
https://theoryclub.github.io/2019/random-alg
https://theoryclub.github.io/2019/random-algblogChromatic Polynomials by Daniel Hathcock<p>Daniel Hathcock gave a talk on the interesting properties of the chromatic polynomials of graphs!</p>
Mon, 25 Mar 2019 04:00:00 +0000
https://theoryclub.github.io/2019/chromatic-poly
https://theoryclub.github.io/2019/chromatic-polyblogAlgebraic Combinatorics by Daniel Hathcock and Sherry Sarkar<p>Daniel and Sherry gave a talk on partially ordered sets and the Sperner property. They went over the proof of Sperner Theorem as well as its applications on some common posets. This meeting was taken from Stanely’s Algebraic Combinatorics book (Chapter 4).</p>
Mon, 11 Mar 2019 04:00:00 +0000
https://theoryclub.github.io/2019/algebraic-comb
https://theoryclub.github.io/2019/algebraic-combblogSturm Sequences by Shyamal Patel<p>Shyamal Patel gave a talk on Sturm sequences and their usefulness in finding roots of polynomials. He described
the motivation for the construction of Sturm sequences as well as several proofs.</p>
Tue, 05 Mar 2019 04:00:00 +0000
https://theoryclub.github.io/2019/strum-sequences
https://theoryclub.github.io/2019/strum-sequencesblogThe Word Problem for Groups & Unsolvability<p>Long time member Eric Zhu is giving a talk on group theory and how it relates to complexity! It will cover the word representation problem along with its connections to undecidability. Here is an abstract :</p>
<p>“In this talk, I will discuss the word problem for groups. First, I will explain what group presentations are, in terms of generators and relations so that no group theory knowledge will be necessary. Then, I will state the word problem and give some examples of how one might go about trying to solve this, including a technique called normal forms and some different algorithms. Then, I will talk about what undecidability means for this problem and the related concept of unsolvability. I will give some examples of group presentations that are unsolvable, but proving why they are unsolvable may be left out due to difficulty. I may also discuss other similar group theoretic decision problems, given the time.”</p>
<p>If you are a student and are interested in giving a talk, please contact our talk coordinator Daniel Hathcock. We are very interested in hearing what the undergraduate student body is studying in Theory CS!</p>
Mon, 25 Feb 2019 04:00:00 +0000
https://theoryclub.github.io/2019/groups-unsolvability
https://theoryclub.github.io/2019/groups-unsolvabilityblogInteractive Proofs and Zero-Knowledge<p>This meeting will be a talk on zero knowledge proofs by the chair of the school of computer science, Dr. Lance Fortnow (also Theory Club’s advisor)!</p>
<p>Interactive Proofs and Zero-Knowledge</p>
<p>King Arthur calls his knights to Camelot to talk about the quest. Some of the knights have been fighting and Arthur needs to sit them at the round table so that only knights who are friends sit next to each other. Arthur has a diagram showing which pairs of knights are friendly but can’t come up with a good seating arrangement. So he calls upon his all-powerful wizard Merlin.</p>
<p>If Merlin can find a good seating arrangement he can just show it to Arthur who can check that only friendly knights sit next to each other. But what if there is no possible arrangement? How does Merlin convince Arthur it is impossible to find a good seating?</p>
<p>We will show that, surprisingly, if Arthur can ask Merlin randomly chosen questions, Merlin can convince Arthur that there is no good seating.</p>
<p>If there is a good seating, we show how Merlin can convince Arthur such a seating exists without revealing any information about the seating itself.</p>
<p>We’ll briefly talk about other results if you have multiple Merlins or very long scrolls that Merlin can write to you can prove far more complex problems and how this ties into the limits of approximation algorithms.</p>
<p>For complexity wonks: The seating example is the NP-complete Hamiltonian Cycle problem. The main results are that co-NP problems have interactive proofs and, under some cryptographic assumptions, NP problems have zero-knowledge interactive proofs.</p>
Mon, 18 Feb 2019 04:00:00 +0000
https://theoryclub.github.io/2019/fortnow-talk
https://theoryclub.github.io/2019/fortnow-talkblogProbabilistic Method Problem Session<p>This meeting is on the probabilistic method problem session in the spirit of Valentine’s day. We went over some interesting bounds on dominating sets and Hamiltonian cycles in tournaments that can be easily derived from the probabilistic method. Check out the slides here : https://drive.google.com/open?id=1hS_qSnxrXiyniuuNB-TNTTGG3ar1lO2Ztyr0veeKRuk</p>
Mon, 11 Feb 2019 04:00:00 +0000
https://theoryclub.github.io/2019/probabilistic-problem-session
https://theoryclub.github.io/2019/probabilistic-problem-sessionblogDistance Preservers<p>This meeting will be a talk on sparse distance preservers of graphs given by Greg Bodwin.</p>
<p><strong>Title:</strong> Distance Preservers</p>
<p><strong>Abstract:</strong>
One of the most fundamental and useful facts in computer science is the existence of BFS trees: given a graph G = (V, E) and a source node s, there is a tree that preserves all pairwise distances in P = {s} x V. But what if we want to preserve distances between an arbitrary set of node pairs, which doesn’t happen to have the structure P = {s} x V? How big does a distance-preserving subgraph then need to be?</p>
<p>In this talk, we will show that the answer is “surprisingly small,” and that in many nontrivial situations you only need O(n) edges in the subgraph. We’ll describe a new yet simple way to think of shortest paths in graphs, escaping the influence of BFS Trees, and we’ll discuss a few open problems on the frontier of research on distance preservers.</p>
Mon, 04 Feb 2019 04:00:00 +0000
https://theoryclub.github.io/2019/sparse-distance-preservers
https://theoryclub.github.io/2019/sparse-distance-preserversblog