Publication

A Fast and Exact Algorithm for the Median-of-Three Problem: A Graph Decomposition Approach

2009
Journal Articles

Abstract

In a previous article, we have shown that adequate subgraphs can be used to decompose multiple breakpoint graphs, achieving a dramatic speedup in solving the median problem. In this article, focusing on the median of three problem, we prove more important properties about adequate subgraphs with rank 3 and discuss the algorithms inventorying simple adequate subgraphs. After finding simple adequate subgraphs of small sizes, we incorporate them into ASMedian, an algorithm to solve the median of three problem. Results on simulated data show dramatic speedup so that many instances can be solved very quickly, even ones containing hundreds or thousands of genes.

Official source

https://infoscience.epfl.ch/entities/publication/94791801-0ef0-4186-819d-bbccbe93129a

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

2009
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/94791801-0ef0-4186-819d-bbccbe93129a

About this result

Related concepts (18)

Median

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of the center.

Geometric median

In geometry, the geometric median of a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the property of minimizing the sum of distances for one-dimensional data, and provides a central tendency in higher dimensions. It is also known as the 1-median, spatial median, Euclidean minisum point, or Torricelli point. The geometric median is an important estimator of location in statistics, where it is also known as the L1 estimator (after the L1 norm).

Tree decomposition

In graph theory, a tree decomposition is a mapping of a graph into a tree that can be used to define the treewidth of the graph and speed up solving certain computational problems on the graph. Tree decompositions are also called junction trees, clique trees, or join trees. They play an important role in problems like probabilistic inference, constraint satisfaction, query optimization, and matrix decomposition. The concept of tree decomposition was originally introduced by .

Related publications (8)

A Fast and Exact Algorithm for the Median-of-Three Problem: A Graph Decomposition Approach

Chat with Graph Search

The Sketching Complexity of Graph and Hypergraph Counting

Robust and Efficient Data Clustering with Signal Processing on Graphs

Graph-based structures in data science : fundamental limits and applications to machine learning