2 research outputs found
Multithreading for the expression-dag-based number type Real_algebraic
Many algorithms, especially in the field of computational geometry, are based
on the premise that arithmetic operations are performed exactly. Real machines
are based on inexact floating-point arithmetic. Various number types have been
developed to close this gap by providing exact computation or ensuring exact
decisions. In this report we describe the implementation of an extension to the
exact-decisions number type Real_algebraic that enables us to take advantage of
multiple processing units.Comment: Technical Repor
Distributed Construction of Light Networks
A -{\em spanner} of a weighted graph is a subgraph that
approximates all pairwise distances up to a factor of . The {\em lightness}
of is defined as the ratio between the weight of to that of the minimum
spanning tree. An -{\em Shallow Light Tree} (SLT) is a tree of
lightness , that approximates all distances from a designated root
vertex up to a factor of . A long line of works resulted in efficient
algorithms that produce (nearly) optimal light spanners and SLTs.
Some of the most notable algorithmic applications of light spanners and SLTs
are in distributed settings. Surprisingly, so far there are no known efficient
distributed algorithms for constructing these objects in general graphs. In
this paper we devise efficient distributed algorithms in the CONGEST model for
constructing light spanners and SLTs, with near optimal parameters.
Specifically, for any and , we show a
-spanner with lightness can be
built in rounds (where
and is the hop-diameter of ). In addition, for any we
provide an -SLT in rounds. The running time of our algorithms cannot be substantially
improved.
We also consider spanners for the family of doubling graphs, and devise a
rounds algorithm in the CONGEST model that
computes a -spanner with lightness . As
a stepping stone, which is interesting in its own right, we first develop a
distributed algorithm for constructing nets (for arbitrary weighted graphs),
generalizing previous algorithms that worked only for unweighted graphs