Cover time and mixing time of random walks on dynamic graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10387271" target="_blank" >RIV/00216208:11320/18:10387271 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1002/rsa.20752" target="_blank" >https://doi.org/10.1002/rsa.20752</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/rsa.20752" target="_blank" >10.1002/rsa.20752</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Cover time and mixing time of random walks on dynamic graphs

Popis výsledku v původním jazyce

The application of simple random walks on graphs is a powerful tool that is useful in many algorithmic settings such as network exploration, sampling, information spreading, and distributed computing. This is due to the reliance of a simple random walk on only local data, its negligible memory requirements, and its distributed nature. It is well known that for static graphs the cover time, that is, the expected time to visit every node of the graph, and the mixing time, that is, the time to sample a node according to the stationary distribution, are at most polynomial relative to the size of the graph. Motivated by real world networks, such as peer-to-peer and wireless networks, the conference version of this paper was the first to study random walks on arbitrary dynamic networks. We study the most general model in which an oblivious adversary is permitted to change the graph after every step of the random walk. In contrast to static graphs, and somewhat counter-intuitively, we show that there are adversary strategies that force the expected cover time and the mixing time of the simple random walk on dynamic graphs to be exponentially long, even when at each time step the network is well connected and rapidly mixing. To resolve this, we propose a simple strategy, the lazy random walk, which guarantees, under minor conditions, polynomial cover time and polynomial mixing time regardless of the changes made by the adversary.

Název v anglickém jazyce

Cover time and mixing time of random walks on dynamic graphs

Popis výsledku anglicky

The application of simple random walks on graphs is a powerful tool that is useful in many algorithmic settings such as network exploration, sampling, information spreading, and distributed computing. This is due to the reliance of a simple random walk on only local data, its negligible memory requirements, and its distributed nature. It is well known that for static graphs the cover time, that is, the expected time to visit every node of the graph, and the mixing time, that is, the time to sample a node according to the stationary distribution, are at most polynomial relative to the size of the graph. Motivated by real world networks, such as peer-to-peer and wireless networks, the conference version of this paper was the first to study random walks on arbitrary dynamic networks. We study the most general model in which an oblivious adversary is permitted to change the graph after every step of the random walk. In contrast to static graphs, and somewhat counter-intuitively, we show that there are adversary strategies that force the expected cover time and the mixing time of the simple random walk on dynamic graphs to be exponentially long, even when at each time step the network is well connected and rapidly mixing. To resolve this, we propose a simple strategy, the lazy random walk, which guarantees, under minor conditions, polynomial cover time and polynomial mixing time regardless of the changes made by the adversary.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Random Structures and Algorithms

ISSN

1042-9832

e-ISSN

—

Svazek periodika

52

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

576-596

Kód UT WoS článku

000438011100003

EID výsledku v databázi Scopus

2-s2.0-85039167104