arXiv subjects

Yuval Emek

Publications and source records attributed to Yuval Emek.

40 records · Page 3Linked to original sources

arXiv2010

Approximating the Statistics of various Properties in Randomly Weighted Graphs

Consider the setting of \emph{randomly weighted graphs}, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, properties of weighted graphs typically become random variables and we are interested in computing their statistical features. Unfortunately, this turns out to be computationally hard for some properties albeit the problem of computing them in the traditional setting of algorithmic graph theory is tractable. For example, there are well known efficient algorithms that compute the \emph{diameter} of a given weighted graph, yet, computing the \emph{expected} diameter of a given randomly weighted graph is \SharpP{}-hard even if the edge weights are identically distributed. In this paper, we define a family of properties of weighted graphs and show that for each property in this family, the problem of computing the \emph{$k^{\text{th}}$ moment} (and in particular, the expected value) of the corresponding random variable in a given randomly weighted graph $G$ admits a \emph{fully polynomial time randomized approximation scheme (FPRAS)} for every fixed $k$. This family includes fundamental properties of weighted graphs such as the diameter of $G$, the \emph{radius} of $G$ (with respect to any designated vertex) and the weight of a \emph{minimum spanning tree} of $G$.

cs.DS↗

arXiv2009

On the Additive Constant of the k-server Work Function Algorithm

We consider the Work Function Algorithm for the k-server problem. We show that if the Work Function Algorithm is c-competitive, then it is also strictly (2c)-competitive. As a consequence of [Koutsoupias and Papadimitriou, JACM 1995] this also shows that the Work Function Algorithm is strictly (4k-2)-competitive.

cs.DS↗

arXiv2008

SINR Diagrams: Towards Algorithmically Usable SINR Models of Wireless Networks

The rules governing the availability and quality of connections in a wireless network are described by physical models such as the signal-to-interference & noise ratio (SINR) model. For a collection of simultaneously transmitting stations in the plane, it is possible to identify a reception zone for each station, consisting of the points where its transmission is received correctly. The resulting SINR diagram partitions the plane into a reception zone per station and the remaining plane where no station can be heard. SINR diagrams appear to be fundamental to understanding the behavior of wireless networks, and may play a key role in the development of suitable algorithms for such networks, analogous perhaps to the role played by Voronoi diagrams in the study of proximity queries and related issues in computational geometry. So far, however, the properties of SINR diagrams have not been studied systematically, and most algorithmic studies in wireless networking rely on simplified graph-based models such as the unit disk graph (UDG) model, which conveniently abstract away interference-related complications, and make it easier to handle algorithmic issues, but consequently fail to capture accurately some important aspects of wireless networks. The current paper focuses on obtaining some basic understanding of SINR diagrams, their properties and their usability in algorithmic applications. Specifically, based on some algebraic properties of the polynomials defining the reception zones we show that assuming uniform power transmissions, the reception zones are convex and relatively well-rounded. These results are then used to develop an efficient approximation algorithm for a fundamental point location problem in wireless networks.

cs.NI↗

arXiv2005

Lower-Stretch Spanning Trees

We prove that every weighted graph contains a spanning tree subgraph of average stretch O((log n log log n)^2). Moreover, we show how to construct such a tree in time O(m log^2 n).

cs.DS↗