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Towards a study of low-complexity graphs Sanjeev Arora, David Steurer, and Avi Wigderson
 

Summary: Towards a study of low-complexity graphs
Sanjeev Arora, David Steurer, and Avi Wigderson
Computer Science Dept, Princeton University, Princeton NJ 08544, USA.
{arora,dsteurer}@cs.princeton.edu.
Institute for Advanced Study, Princeton NJ.
avi@ias.edu
Abstract. We propose the study of graphs that are defined by low-
complexity distributed and deterministic agents. We suggest that this
viewpoint may help introduce the element of individual choice in models
of large scale social networks. This viewpoint may also provide interesting
new classes of graphs for which to design algorithms.
We focus largely on the case where the "low complexity" computation is
AC0
. We show that this is already a rich class of graphs that includes
examples of lossless expanders and power-law graphs. We give evidence
that even such low complexity graphs present a formidable challenge
to algorithms designers. On the positive side, we show that many algo-
rithms from property testing and data sketching can be adapted to give
meaningful results for low-complexity graphs.
1 Introduction

  

Source: Arora, Sanjeev - Department of Computer Science, Princeton University
Wigderson, Avi - Institute for Advanced Study, Princeton University

 

Collections: Computer Technologies and Information Sciences; Mathematics