Analysing local algorithms in location-aware quasi-unit-disk graphs


Autoria(s): Hassinen, Marja; Kaasinen, Joel; Kranakis, Evangelos; Polishchuk, Valentin; Suomela, Jukka; Wiese, Andreas
Contribuinte(s)

University of Helsinki, Department of Computer Science (-2009)

University of Helsinki, Helsinki Institute for Information Technology HIIT

University of Helsinki, Helsinki Institute for Information Technology HIIT

Data(s)

2011

Resumo

A local algorithm with local horizon r is a distributed algorithm that runs in r synchronous communication rounds; here r is a constant that does not depend on the size of the network. As a consequence, the output of a node in a local algorithm only depends on the input within r hops from the node. We give tight bounds on the local horizon for a class of local algorithms for combinatorial problems on unit-disk graphs (UDGs). Most of our bounds are due to a refined analysis of existing approaches, while others are obtained by suggesting new algorithms. The algorithms we consider are based on network decompositions guided by a rectangular tiling of the plane. The algorithms are applied to matching, independent set, graph colouring, vertex cover, and dominating set. We also study local algorithms on quasi-UDGs, which are a popular generalisation of UDGs, aimed at more realistic modelling of communication between the network nodes. Analysing the local algorithms on quasi-UDGs allows one to assume that the nodes know their coordinates only approximately, up to an additive error. Despite the localisation error, the quality of the solution to problems on quasi-UDGs remains the same as for the case of UDGs with perfect location awareness. We analyse the increase in the local horizon that comes along with moving from UDGs to quasi-UDGs.

Identificador

http://hdl.handle.net/10138/27935

0166-218X

Idioma(s)

eng

Publicador

Elsevier B. V.

Relação

Discrete Applied Mathematics

Fonte

Hassinen , M , Kaasinen , J , Kranakis , E , Polishchuk , V , Suomela , J & Wiese , A 2011 , ' Analysing local algorithms in location-aware quasi-unit-disk graphs ' Discrete Applied Mathematics , vol 159 , no. 15 , pp. 1566–1580 . , 10.1016/j.dam.2011.05.004

Palavras-Chave #113 Computer and information sciences #111 Mathematics
Tipo

A1 Refereed journal article

info:eu-repo/semantics/article

info:eu-repo/semantics/acceptedVersion