Many distances in planar graphs

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Title:	Many distances in planar graphs
Authors:	ID Cabello, Sergio (Author)
Files:	http://www.imfm.si/preprinti/PDF/01089.pdf
Language:	English
Work type:	Not categorized
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	We show how to compute in $O(n^{4/3} log^{1/3} n + n^{2/3}k^{2/3} log n)$ time the distance between $k$ given pairs of vertices of a planar graph $G$ with $n$ vertices. This improves previous results whenever $(n/log n)^{5/6} le k le n^2/log^6 n$ . As an application, we speed up previous algorithms for computing the dilation of geometric planar graphs.
Keywords:	matematika, teorija grafov, ravninski graf, razdalja, mathematics, graph theory, planar graph, distance
Year of publishing:	2009
Number of pages:	str. 1-18
Numbering:	Vol. 47, št. 1089
PID:	20.500.12556/DKUM-51785
ISSN:	1318-4865
UDC:	519.17
COBISS.SI-ID:	15142233
NUK URN:	URN:SI:UM:DK:HBH2ZYTR
Publication date in DKUM:	10.07.2015
Views:	1402
Downloads:	78
Metadata:
Categories:	Misc.
:	CABELLO, Sergio, 2009, Many distances in planar graphs [online]. 2009. [Accessed 31 March 2025]. Retrieved from: http://www.imfm.si/preprinti/PDF/01089.pdf Copy citation