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From Computational Complexity
#### Is the complexity of approximating Vertex Cover of degree 3 open?

RECALL:A max-problem f has a A P Time App Scheme (PTAS) if there is an algorithm ALG such that ALG(\epsilon) \ge (1-\epsilon)f(x).A min-problem f has a A P Time...

From Computational Complexity
#### POSTED UPDATED VERSION OF Computers and Intractability: A guide to Algorithmic Lower Bounds posted (New title)

We have posted a revised version of Computational Intractability: A Guide to Algorithmic Lower Boundsby Demaine-Gasarch-HajiaghayiThe book is here.(For the original...

From Computational Complexity
#### There are two different definitions of Integer Programming. Why?

Alice and Bob have the following conversation.===============================ALICE: In your book you define INT PROG as, given a matrix A and vectors b,c,find the...

From Computational Complexity
#### Monarachy: A Problem with Definitions

As I am sure you know, Queen Elizabeth II passed away at the age of 96 recently. I am not a royal-watcher, but I am a royal-watcher-watcher. That is, the question...

From Computational Complexity
#### Computers and Intractability: A Guide to Algorithmic Lower Bounds. First draft available! Comments Welcome!

(This post is written by Erik Demaine, William Gasarch, and Mohammad Hajiaghayi)In 1979 Garey and Johnson published the classic Computers and Intractability...

From Computational Complexity
#### A non-controversial question about the Documents Donald Trump had in his house

This is a non-partisan post. In the interest of disclosure I will divulge that I do not think private citizens should have top secret government documents in their...

From Computational Complexity
#### The Held Prize for comb. opt. AND Disc Opt AND Alg AND Complexity theory AND related parts of CS.

Dan Spielman asked me to blog about the Held Prize. I first present what he send me, and then have some thoughts.FROM DAN: ------------------------------------...

From Computational Complexity
#### Juris Hartmanis passed away on July 29 at the age of 94

Juris Hartmanis, one of the founders of Complexity Theory, passed away on July 29 at the age of 94. The Gödel's Last Letter blog has an obit posted here. When...

From Computational Complexity
#### 100 Best Number Theory books of all Time---except many are not on Number Theory

I was recently emailed this link:
100 Best Number Theory books of all Time
That sounds like a good list to have! But then I looked at it. The issue IS NOT that...

From Computational Complexity
#### What is known about that sequence

In my last post I wrote:---------------------------Consider the recurrencea_1=1for all n\ge 2, a_n = a_{n-1} + a_{n/2}.For which M does this recurrence have infinitely...

From Computational Complexity
#### An open question about a sequence mod M.

In this post n/2 means floor{n/2}Consider the recurrencea_1=1for all n\ge 2, a_n = a_{n-1} + a_{n/2}.For which M does this recurrence have infinitely many n such...

From Computational Complexity
#### Review of The Engines of Cognition: Essays From the LessWrong Forum/Meta question about posts

A while back I reviewed A Map that Reflects the Territory which is a collection of essays posted on the lesswrong forum. My review is here. I posted it to both...

From Computational Complexity
#### Counting the Number of 3-colorings of a graph is Sharp-P complete. This should be better known.

BILL: Lance, is #3COL #P complete? (#3COL is: Given a graph G, return the number of different 3-colorings it has.) LANCE: Surely you know that for all naturalnatural...

From Computational Complexity
#### Guest post by Prahalad Rajkumar: advice for grad students

I suspect that Lance and/or I have had blogs giving advice to grad students. I won't point to any particular posts since that's a hard thing to search for. However...

From Computational Complexity
#### I am surprised that the Shortest Vector Problem is not known to be NP-hard, but perhaps I am wrong

A lattice L in R^n is a discrete subgroup of R^n. Let p IN [1,infinty)The p-norm of a vector x=(x_1,...,x_n) IN R^n is here...

From Computational Complexity
#### Does the Social Media Law in Texas affect theory bloggers?

A new law in Texas states that any social media sites that has at least 50 million subscribers a month cannot ban anyone (its more nuanced than that, but that's...

From Computational Complexity
#### Discussions I wish we were having

1) Democrats think the best way to avoid school shootings (and other problems with guns) is to have regulations on Guns. They have proposed legislation. The Republicans...

From Computational Complexity
#### In the 1960's students protested the Vietnam war!/In 1830 students protested... Math?

I was at SUNY Stonybrook for college 1976-1980. I remember one student protest about a change to the calendar that (I think) would have us go home for winter break...

From Computational Complexity
#### Is Kamala Harris our first female PREZ? No. Do I have a theorem named after me. No. But in both cases...

On Nov 19, 2021 Joe Biden got a colonoscopy and hence the 25th amendment was used to make Kamala Harris the president temporarily (this source: here says 85 minutes...

From Computational Complexity
#### Queen Elizabeth is the 3rd longest reigning monarch; The problem with definitions

A few days ago Queen Elizabeth passed Johann II of Liechtenstein to be the third longest reigning monarch (see here). A summary of the top 4:4) Johann II, Liechtenstein...