Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, July 22, 2008, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Jeong Han Kim (Yonsei Univ., South Korea)

Optimal Query Complexity Bounds for Finding Graphs

We consider the problem of finding an unknown graph by using two types of queries with an additive property. Given a graph, an additive query asks the number of edges in a set of vertices while a cross-additive query asks the number of edges crossing between two disjoint sets of vertices. The queries ask sum of weights for the weighted graphs. These types of queries were partially motivated in DNA shotgun sequencing and linkage discovery problem of artificial intelligence.

For a given unknown weighted graph $G$ with $n$ vertices, $m$ edges, and a certain mild condition on weights, we prove that there exists a non-adaptive algorithm to find the edges of $G$ using $O\left(\frac{m\log{n}}{\log{m}}\right)$ queries of both types provided that $m \geq n^{\epsilon}$ for any constant $\epsilon> 0$. For a graph, it is shown that the same bound holds for all range of $m$.

This settles a conjecture of Grebinski for finding an unweighted graph using additive queries. We also consider the problem of finding the Fourier coefficients of a certain class of pseudo-Boolean functions. A similar coin weighing problem is also considered.

Joint work with S. Choi.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login