### Recent Comments

Gil Kalai on זה הזמן לשינוי Yiftach on זה הזמן לשינוי Gil Kalai on זה הזמן לשינוי Yiftach on זה הזמן לשינוי Gil Kalai on זה הזמן לשינוי קוסמופוליט on זה הזמן לשינוי Gil Kalai on זה הזמן לשינוי Eli_B on זה הזמן לשינוי Michael Elkin on זה הזמן לשינוי Gil Kalai on זה הזמן לשינוי Eli_B on זה הזמן לשינוי Gil Kalai on זה הזמן לשינוי -
### Recent Posts

- זה הזמן לשינוי
- Combinatorics and More – Greatest Hits
- Ilan and me
- The Simplex, the Cyclic polytope, the Positroidron, the Amplituhedron, and Beyond
- From Oberwolfach: The Topological Tverberg Conjecture is False
- Midrasha Mathematicae #18: In And Around Combinatorics
- Quantum computing: achievable reality or unrealistic dream
- A Historical Picture Taken by Nimrod Megiddo
- Scott Triumphs* at the Shtetl

### Top Posts & Pages

- זה הזמן לשינוי
- The Simplex, the Cyclic polytope, the Positroidron, the Amplituhedron, and Beyond
- Believing that the Earth is Round When it Matters
- Quantum computing: achievable reality or unrealistic dream
- The Kadison-Singer Conjecture has beed Proved by Adam Marcus, Dan Spielman, and Nikhil Srivastava
- Midrasha Mathematicae #18: In And Around Combinatorics
- When It Rains It Pours
- Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
- Five Open Problems Regarding Convex Polytopes

### RSS

# Tag Archives: Linear programming

## Projections to the TSP Polytope

Michael Ben Or told me about the following great paper Linear vs. Semidefinite Extended Formulations: Exponential Separation and Strong Lower Bounds by Samuel Fiorini, Serge Massar, Sebastian Pokutta, Hans Raj Tiwary and Ronald de Wolf. The paper solves an old conjecture … Continue reading

## IPAM remote blogging: The Many Facets of Linear Programming

The many facets of Linear Programming Here is an extremely nice paper by Michael Todd from 2001. It gives useful background for many lectures and it can serve as a good base point to examine last decade’s progress. Background post for … Continue reading

## Günter Ziegler: 1000$ from Beverly Hills for a Math Problem. (IPAM remote blogging.)

Scanned letter by Zadeh. (c) Günter M. Ziegler left-to-right: David Avis, Norman Zadeh, Oliver Friedmann, and Russ Caflish (IPAM director). Photo courtesy Eddie Kim. Update: The slides for Friedmann’s talk are now available. The conference schedule page contains now the slides for … Continue reading

Posted in Computer Science and Optimization, Conferences, Guest blogger
Tagged Linear programming
4 Comments

## Subexponential Lower Bound for Randomized Pivot Rules!

Oliver Friedmann, Thomas Dueholm Hansen, and Uri Zwick have managed to prove subexponential lower bounds of the form for the following two basic randomized pivot rules for the simplex algorithm! This is the first result of its kind and deciding … Continue reading

## The Polynomial Hirsch Conjecture: A proposal for Polymath3

This post is continued here. Eddie Kim and Francisco Santos have just uploaded a survey article on the Hirsch Conjecture. The Hirsch conjecture: The graph of a d-polytope with n vertices facets has diameter at most n-d. We devoted several … Continue reading

## A Diameter problem (7): The Best Known Bound

Our Diameter problem for families of sets Consider a family of subsets of size d of the set N={1,2,…,n}. Associate to a graph as follows: The vertices of are simply the sets in . Two vertices and are adjacent if . … Continue reading

## A Diameter Problem (6): Abstract Objective Functions

George Dantzig and Leonid Khachyan In this part we will not progress on the diameter problem that we discussed in the earlier posts but will rather describe a closely related problem for directed graphs associated with ordered families of sets. The role models for … Continue reading

Posted in Combinatorics, Convex polytopes, Open problems
Tagged Hirsch conjecture, Linear programming
7 Comments

## Diameter Problem (3)

3. What we will do in this post and and in future posts We will now try all sorts of ideas to give good upper bounds for the abstract diameter problem that we described. As we explained, such bounds apply … Continue reading

Posted in Combinatorics, Convex polytopes, Open problems
Tagged Hirsch conjecture, Linear programming, Quasi-automated proofs
1 Comment