{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article1239","name":"Approximating Average Parameters of Graphs","abstract":"Inspired by Feige (36th STOC, 2004), we initiate a study of sublinear randomized algorithms for approximating average parameters of a graph. \r\nSpecifically, we consider the average degree of a graph and the average distance between pairs of vertices in a graph. \r\nSince our focus is on sublinear algorithms, these algorithms access the input graph via queries to an adequate oracle. \r\n\r\nWe consider two types of queries.\r\nThe first type is standard neighborhood queries (i.e., what is the i'th neighbor of vertex v?), whereas the second type are queries regarding the quantities that we need to find the average of (i.e., what is the degree of vertex v? and what is the distance between u and v, respectively).\r\n\r\nLoosely speaking, our results indicate a difference between the two problems: For approximating the average degree, the standard neighbor queries suffice and in fact are preferable to degree queries. In contrast, for approximating average distances, the standard neighbor queries are of little help whereas distance queries are crucial.","keywords":["Graph parameters","degree","distance"],"author":[{"@type":"Person","name":"Goldreich, Oded","givenName":"Oded","familyName":"Goldreich"},{"@type":"Person","name":"Ron, Dana","givenName":"Dana","familyName":"Ron"}],"position":2,"pageStart":1,"pageEnd":0,"dateCreated":"2006-08-28","datePublished":"2006-08-28","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Goldreich, Oded","givenName":"Oded","familyName":"Goldreich"},{"@type":"Person","name":"Ron, Dana","givenName":"Dana","familyName":"Ron"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.05291.2","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume576","volumeNumber":5291,"name":"Dagstuhl Seminar Proceedings, Volume 5291","dateCreated":"2006-08-28","datePublished":"2006-08-28","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article1239","isPartOf":{"@type":"Periodical","@id":"#series119","name":"Dagstuhl Seminar Proceedings","issn":"1862-4405","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume576"}}}