[Colloquium] REMINDER: Research at TTIC: Yury Makarychev, TTIC

[Dawn Ellis]

When:     Friday, January 23rd at noon

Where:    TTIC, 6045 S Kenwood Avenue, 5th Floor, Room 526

Who:       Yury Makarychev, TTIC

Title:       Nonuniform Graph Partitioning with Unrelated Weights

Abstract:

We give a bi-criteria approximation algorithm for the Minimum Nonuniform
Partitioning problem, recently introduced by Krauthgamer, Naor, Schwartz
and Talwar (2014). In this problem, we are given a graph $G=(V,E)$ on $n$
vertices and $k$ numbers $\rho_1,\dots, \rho_k$. The goal is to partition
the graph into $k$ disjoint sets $P_1,\dots, P_k$ satisfying $|P_i|\leq
\rho_i n$ so as to minimize the number of edges cut by the partition. Our
algorithm has an approximation ratio of $O(\sqrt{\log n \log k})$ for
general graphs, and an $O(1)$ approximation for graphs with excluded
minors. This is an improvement upon the $O(\log n)$ algorithm of
Krauthgamer, Naor, Schwartz and Talwar (2014). Our approximation ratio
matches the best known ratio for the Minimum (Uniform) $k$-Partitioning
problem.

We extend our results to the case of "unrelated weights" and to the case of
"unrelated $d$-dimensional weights". In the former case, different vertices
may have different weights and the weight of a vertex may depend on the set
$P_i$ the vertex is assigned to. In the latter case, each vertex $u$ has a
$d$-dimensional weight $r(u,i) = (r_1(u,i), \dots, r_d(u,i))$ if $u$ is
assigned to $P_i$. Each set $P_i$ has a $d$-dimensional capacity $c(i) =
(c_1(i),\dots, c_d(i))$. The goal is to find a partition such that
$\sum_{u\in {P_i}} r(u,i) \leq c(i)$ coordinate-wise.

Joint work with Konstantin Makarychev



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Research at TTIC Seminar Series

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-- 
*Dawn Ellis*
Administrative Coordinator,
Bookkeeper
773-834-1757
dellis at ttic.edu

TTIC
6045 S. Kenwood Ave.
Chicago, IL. 60637
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