More Analysis of Double Hashing for Balanced Allocations

With double hashing, for a key $x$, one generates two hash values $f(x)$ and $g(x)$, and then uses combinations $(f(x) +i g(x)) \bmod n$ for $i=0,1,2,...$ to generate multiple hash values in the range $[0,n-1]$ from the initial two. For balanced allocations, keys are hashed into a hash table where each bucket can hold multiple keys, and each key is placed in the least loaded of $d$ choices. It has been shown previously that asymptotically the performance of double hashing and fully random hashing is the same in the balanced allocation paradigm using fluid limit methods. Here we extend a coupling argument used by Lueker and Molodowitch to show that double hashing and ideal uniform hashing are asymptotically equivalent in the setting of open address hash tables to the balanced allocation setting, providing further insight into this phenomenon. We also discuss the potential for and bottlenecks limiting the use this approach for other multiple choice hashing schemes.Comment: 13 pages ; current draft ; will be submitted to conference shortl

Scheduling with Predictions and the Price of Misprediction

In many traditional job scheduling settings, it is assumed that one knows the time it will take for a job to complete service. In such cases, strategies such as shortest job first can be used to improve performance in terms of measures such as the average time a job waits in the system. We consider the setting where the service time is not known, but is predicted by for example a machine learning algorithm. Our main result is the derivation, under natural assumptions, of formulae for the performance of several strategies for queueing systems that use predictions for service times in order to schedule jobs. As part of our analysis, we suggest the framework of the "price of misprediction," which offers a measure of the cost of using predicted information

Simple Load Balancing for Distributed Hash Tables

Distributed hash tables have recently become a useful building block for a variety of distributed applications. However, current schemes based upon consistent hashing require both considerable implementation complexity and substantial storage overhead to achieve desired load balancing goals. We argue in this paper that these goals can b e achieved more simply and more cost-effectively. First, we suggest the direct application of the "power of two choices" paradigm, whereby an item is stored at the less loaded of two (or more) random alternatives. We then consider how associating a small constant number of hash values with a key can naturally b e extended to support other load balancing methods, including load-stealing or load-shedding schemes, as well as providing natural fault-tolerance mechanisms