Bounds on the Geometric Mean of Arc Lengths for Bounded-Degree Planar Graphs
نویسندگان
چکیده
Data access time becomes the main bottleneck in applications dealing with large-scale graphs. Cache-oblivious layouts, constructed to minimize the geometric mean of arc lengths of graphs, have been adapted to reduce data access time during random walks on graphs. In this paper, we present a constant factor approximation algorithm for the Minimum Geometric Mean Layout (MGML) problem for bounded-degree planar graphs. We also derive an upper bound for any layout of the MGML problem. To the best of our knowledge, these are the first results for the MGML problem with bounded-degree planar graphs.
منابع مشابه
On the total version of geometric-arithmetic index
The total version of geometric–arithmetic index of graphs is introduced based on the endvertex degrees of edges of their total graphs. In this paper, beside of computing the total GA index for some graphs, its some properties especially lower and upper bounds are obtained.
متن کاملBoundaries of Planar Graphs, via Circle Packings
We provide a geometric representation of the Poisson and Martin boundaries of a transient, bounded degree triangulation of the plane in terms of its circle packing in the unit disc (this packing is unique up to Möbius transformations). More precisely, we show that any bounded harmonic function on the graph is the harmonic extension of some measurable function on the boundary of the disk, and th...
متن کاملThe second geometric-arithmetic index for trees and unicyclic graphs
Let $G$ be a finite and simple graph with edge set $E(G)$. The second geometric-arithmetic index is defined as $GA_2(G)=sum_{uvin E(G)}frac{2sqrt{n_un_v}}{n_u+n_v}$, where $n_u$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$. In this paper we find a sharp upper bound for $GA_2(T)$, where $T$ is tree, in terms of the order and maximum degree o...
متن کاملOn Geometric Spanners of Euclidean Graphs and their Applications in Wireless Networks
We consider the problem of constructing a bounded-degree planar geometric spanner for a unit disk graph modeling a wireless network. The related problem of constructing a planar geometric spanner of a Euclidean graph has been extensively studied in the literature. It is well known that the Delaunay subgraph is a planar geometric spanner with stretch factor ; however, its degree may not be bound...
متن کاملOn the M-polynomial of planar chemical graphs
Let $G$ be a graph and let $m_{i,j}(G)$, $i,jge 1$, be the number of edges $uv$ of $G$ such that ${d_v(G), d_u(G)} = {i,j}$. The $M$-polynomial of $G$ is $M(G;x,y) = sum_{ile j} m_{i,j}(G)x^iy^j$. With $M(G;x,y)$ in hands, numerous degree-based topological indices of $G$ can be routinely computed. In this note a formula for the $M$-polynomial of planar (chemical) graphs which have only vertices...
متن کامل