On small-depth tree augmentations

نویسندگان

چکیده

We study the Weighted Tree Augmentation Problem for general link costs. show that integrality gap of odd-LP relaxation (weighted) a k-level tree instance is at most 2−12k−1. For 2- and 3-level trees, these ratios are 32 74 respectively. Our proofs constructive yield polynomial-time approximation algorithms with matching guarantees.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On Small Depth Threshold Circuits

In this talk we will consider various classes defined by small depth polynomial size circuits which contain threshold gates and parity gates. We will describe various inclusions between many classes defined in this way and also classes whose definitions rely upon spectral properties of Boolean functions.

متن کامل

On the tree-depth of Random Graphs

The tree–depth is a parameter introduced under several names as a measure of sparsity of a graph. We compute asymptotic values of the tree–depth of random graphs. For dense graphs, p n−1, the tree–depth of a random graph G is a.a.s. td(G) = n − O( √ n/p). Random graphs with p = c/n, have a.a.s. linear tree–depth when c > 1, the tree–depth is Θ(log n) when c = 1 and Θ(log log n) for c < 1. The r...

متن کامل

On Maintaining Online Bipartite Matchings with Augmentations

In the thesis we focus on an algorithmic approach to one of many problems related to resource allocation. More precisely, its main result is a procedure for maintaining a maximum cardinality matching in a setting, where a part of the graph is revealed online, during the algorithm run. A matching M in a graph G = 〈V ,E〉 is any subset of edges M ⊆ E that are pairwise vertex-disjoint, i.e., each v...

متن کامل

Concave Flow on Small Depth Directed Networks

Small depth networks arise in a variety of network related applications, often in the form of maximum flow and maximum weighted matching. Recent works have generalized such methods to include costs arising from concave functions. In this paper we give an algorithm that takes a depth D network and strictly increasing concave weight functions of flows on the edges and computes a (1−ǫ)-approximati...

متن کامل

On the Power of Small-Depth Computation

In this work we discuss selected topics on small-depth computation, presenting a few unpublished proofs along the way. The four chapters contain: 1. A unified treatment of the challenge of exhibiting explicit functions that have small correlation with low-degree polynomials over {0, 1}. 2. An unpublished proof that small bounded-depth circuits (AC) have exponentially small correlation with the ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Operations Research Letters

سال: 2022

ISSN: ['0167-6377', '1872-7468']

DOI: https://doi.org/10.1016/j.orl.2022.10.002