Name
Abstract | ||
|---|---|---|
The study of {\em balls-into-bins processes} or {\em occupancy problems} has
a long history. These processes can be used to translate realistic problems
into mathematical ones in a natural way. In general, the goal of a
balls-into-bins process is to allocate a set of independent objects (tasks,
jobs, balls) to a set of resources (servers, bins, urns) and, thereby, to
minimize the maximum load. In this paper, we analyze the maximum load for the
{\em chains-into-bins} problem, which is defined as follows. There are $n$
bins, and $m$ objects to be allocated. Each object consists of balls connected
into a chain of length $\ell$, so that there are $m \ell$ balls in total. We
assume the chains cannot be broken, and that the balls in one chain have to be
allocated to $\ell$ consecutive bins. We allow each chain $d$ independent and
uniformly random bin choices for its starting position. The chain is allocated
using the rule that the maximum load of any bin receiving a ball of that chain
is minimized. We show that, for $d \ge 2$ and $m\cdot\ell=O(n)$, the maximum
load is $((\ln \ln m)/\ln d) +O(1)$ with probability $1-\tilde O(1/m^{d-1})$. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.jda.2011.12.006 | Clinical Orthopaedics and Related Research |
Keywords | DocType | Volume |
chains-into-bins process,occupancy problem,consecutive bin,m object,balls-into-bins process,random bin choice,long history,n bin,independent object,chains-into-bins problem,maximum load,random processes | Journal | 14, |
Citations | PageRank | References |
0 | 0.34 | 9 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tugkan Batu | 1 | 346 | 24.83 |
| Petra Berenbrink | 2 | 472 | 46.41 |
| Colin Cooper | 3 | 857 | 91.88 |