Tata Institute of Fundamental Research
An Approximate Generalization of the Okamura-Seymour Theorem
STCS Seminar
Speaker:
Nikhil Kumar (Hasso-Plattner institute, Potsdam, Germany.)
Organiser:
Jatin Batra
Date:
Tuesday, 31 Jan 2023, 09:30 to 10:30
Venue:
A201
(Scan to add to calendar)
Abstract:
We consider the problem of multicommodity flows in planar graphs. Okamura and Seymour showed that if all the demands are incident on one face, then the cut-condition is sufficient for routing demands. We consider the following generalization of this setting and prove an approximate max flow-min cut theorem: for every demand edge, there exists a face containing both its end points. We show that the cut-condition is sufficient for routing Ω(1) -fraction of all the demands. To prove this, we give a L1-embedding of the planar metric which approximately preserves distance between all pair of points on the same face.
| Speaker: | Nikhil Kumar (Hasso-Plattner institute, Potsdam, Germany.) |
| Organiser: | Jatin Batra |
| Date: | Tuesday, 31 Jan 2023, 09:30 to 10:30 |
| Venue: | A201 |
(Scan to add to calendar)
Abstract:
We consider the problem of multicommodity flows in planar graphs. Okamura and Seymour showed that if all the demands are incident on one face, then the cut-condition is sufficient for routing demands. We consider the following generalization of this setting and prove an approximate max flow-min cut theorem: for every demand edge, there exists a face containing both its end points. We show that the cut-condition is sufficient for routing Ω(1) -fraction of all the demands. To prove this, we give a L1-embedding of the planar metric which approximately preserves distance between all pair of points on the same face.