Projekteja vuodessa
Abstrakti
The landscape of the distributed time complexity is nowadays wellunderstood for subpolynomial complexities. When we look at deterministic algorithms in the LOCAL model and locally checkable problems (LCLs) in boundeddegree graphs, the following picture emerges:There are lots of problems with time complexities of Θ(log ^{∗}n) or Θ(log n).It is not possible to have a problem with complexity between ω(log ^{∗}n) and o(log n).In general graphs, we can construct LCL problems with infinitely many complexities between ω(log n) and n^{o}^{(}^{1}^{)}.In trees, problems with such complexities do not exist. However, the high end of the complexity spectrum was left open by prior work. In general graphs there are LCL problems with complexities of the form Θ(n^{α}) for any rational 0 < α≤ 1 / 2 , while for trees only complexities of the form Θ(n^{1}^{/}^{k}) are known. No LCL problem with complexity between ω(n) and o(n) is known, and neither are there results that would show that such problems do not exist. We show that:In general graphs, we can construct LCL problems with infinitely many complexities between ω(n) and o(n).In trees, problems with such complexities do not exist. Put otherwise, we show that any LCL with a complexity o(n) can be solved in time O(n) in trees, while the same is not true in general graphs.
Alkuperäiskieli  Englanti 

Sivut  259281 
Sivumäärä  23 
Julkaisu  DISTRIBUTED COMPUTING 
Vuosikerta  34 
Numero  4 
DOI  pysyväislinkit  
Tila  Julkaistu  elokuuta 2021 
OKMjulkaisutyyppi  A1 Julkaistu artikkeli, soviteltu 
Sormenjälki
Sukella tutkimusaiheisiin 'Almost global problems in the LOCAL model'. Ne muodostavat yhdessä ainutlaatuisen sormenjäljen.Projektit
 1 Päättynyt

Hajautetun laskennan aikavaativuuden kartoittaminen
Hirvonen, J., Purcell, C., Suomela, J., Korhonen, J., Balliu, A., Olivetti, D. & Rabie, M.
01/09/2015 → 31/08/2019
Projekti: Academy of Finland: Other research funding