Big O Theory ClubThoughts on theoretical computer science and research life.
https://theoryclub.github.io/
Sun, 17 Feb 2019 23:03:02 +0000Sun, 17 Feb 2019 23:03:02 +0000Jekyll v3.7.4Interactive 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-preserversblogDonut Problem Session<p>First meeting of the semester was a problem session! We had donuts as well as a few very interesting problems about
discrete structures, probability, and set theory. The slides for the problem session are <a href="https://docs.google.com/presentation/d/1cAq-9GU3H-qxc3b5Mr-9oRnub0Dqy35unSzF9FrdEpw/edit?usp=sharing">here</a></p>
<p>All of the problems in one nice pdf are <a href="/files/DonutProblemSession.pdf">here</a>.</p>
Mon, 14 Jan 2019 04:00:00 +0000
https://theoryclub.github.io/2019/donut-problem-session
https://theoryclub.github.io/2019/donut-problem-sessionblogDeletion Codes<p>For our final meeting of the semester, we had professor Venkat Guruswami present a talk on deletion codes, a subset of error-correction codes. Thank you to everyone who came to Big O this semester! We’ll see you next year!</p>
<p>The slides for the talk are <a href="/files/deletion-codes.pptx">here</a>.</p>
Mon, 03 Dec 2018 04:00:00 +0000
https://theoryclub.github.io/2018/deletion-codes
https://theoryclub.github.io/2018/deletion-codesblogOracles in Complexity Theory<p>A guest appearance by our faculty talks coordinator DeVon, we had an introduction to oracles. Additionally, he talked about Bounded Error Quantum Polynomial Time (BQP) vs. Polynomial Hierarchy (PH) and barriers to proofs in complexity theory. The slides are <a href="/files/oraclescomplexity.pptx">here</a>.</p>
Mon, 26 Nov 2018 04:00:00 +0000
https://theoryclub.github.io/2018/oracles
https://theoryclub.github.io/2018/oraclesblogHappy Ending Problem<p>This week, Sherry gave a lecture/problem session on the Happy Ending Problem, a popular field of mathematics created by P. Erdös, G. Szekeres, and E. Klein. This problem is very interesting for its connections to Ramsey theory. Her main reference is this <a href="http://neeldhara.com/ramblings/notes/cgt-01">website</a>.</p>
Mon, 19 Nov 2018 04:00:00 +0000
https://theoryclub.github.io/2018/happy-ending
https://theoryclub.github.io/2018/happy-endingblogMarkov Chain Monte Carlo Methods<p>Yet another faculty talk, this week we had and introduction to Markov Chain Monte Carlo methods by Dr. Eric Vigoda! MCMC methods are super useful in approximating the size #P to count sets, the volume of hard to calculate integrals, and more.</p>
Mon, 12 Nov 2018 04:00:00 +0000
https://theoryclub.github.io/2018/monte-carlo
https://theoryclub.github.io/2018/monte-carloblogSpectral Algorithms<p>We had another faculty talk this week, about how graphs, linear algebra, and algorithms come together in Spectral Algorithms by Dr. Richard Peng. Here is the full abstract:</p>
<p>The study of large scale data sets in machine learning, statistics, and scientific computing is making increasing use of high performance algorithmic primitives. Tools such as linear systems solvers and convex optimization solvers are integrated in programming languages such as MATLAB, Python, and Julia, and taught as programming constructs in classes. On the other hand, the ever-increasing scale of data, as well as growth in data sources, creates a multitude of new challenges for these primitives: the running times of many, if not most, implementations of linear system solvers and convex optimization tools scale super-linearly with input sizes.
Over the past three decades, works related to efficient solvers for a class of graph structured matrices, graph Laplacians, led to fundamental results in combinatorial optimization and scientific computing as well as the Laplacian paradigm for graph algorithms. In this talk I will survey these progresses, with focus on the underlying algorithm design approaches. Specifically, I will discuss the origin of algorithms that combine combinatorial and numerical building blocks via spectral graph theory, and describe recent efforts on designing new tools tailored towards the overall algorithmic questions.</p>
Mon, 05 Nov 2018 04:00:00 +0000
https://theoryclub.github.io/2018/spectral-algorithms
https://theoryclub.github.io/2018/spectral-algorithmsblogSpooky Problem Session<p>Happy Halloween! We had an adeptly themed problem session led by Arvind this week! You can find the problems <a href="https://docs.google.com/presentation/d/1hmR_X0NY--Zuu3L6LPkOXNbxNwck9BKCCVIPBvDCHE8/edit?usp=sharing">here</a>.</p>
Mon, 29 Oct 2018 04:00:00 +0000
https://theoryclub.github.io/2018/spooky-problem-session
https://theoryclub.github.io/2018/spooky-problem-sessionblog