Consistent Hashing with Bounded Loads (1608.01350v3)

Abstract: Designing algorithms for balanced allocation of clients to servers in dynamic settings is a challenging problem for a variety of reasons. Both servers and clients may be added and/or removed from the system periodically, and the main objectives of allocation algorithms are: the uniformity of the allocation, and the number of moves after adding or removing a server or a client. The most popular solution for our dynamic settings is Consistent Hashing. However, the load balancing of consistent hashing is no better than a random assignment of clients to servers, so with $n$ of each, we expect many servers to be overloaded with $\Theta(\log n/ \log\log n)$ clients. In this paper, with $n$ clients and $n$ servers, we get a guaranteed max-load of 2 while only moving an expected constant number of clients for each update. We take an arbitrary user specified balancing parameter $c=1+\epsilon>1$. With $m$ balls and $n$ bins in the system, we want no load above $\lceil cm/n\rceil$. Meanwhile we want to bound the expected number of balls that have to be moved when a ball or server is added or removed. Compared with general lower bounds without capacity constraints, we show that in our algorithm when a ball or bin is inserted or deleted, the expected number of balls that have to be moved is increased only by a multiplicative factor $O({1\over \epsilon^2})$ for $\epsilon \le 1$ (Theorem 4) and by a factor $1+O(\frac{\log c}c)$ for $\epsilon\ge 1$ (Theorem 3). Technically, the latter bound is the most challenging to prove. It implies that we for superconstant $c$ only pay a negligible cost in extra moves. We also get the same bounds for the simpler problem where we instead of a user specified balancing parameter have a fixed bin capacity $C$ for all bins.

• The paper's main contribution is a novel hashing algorithm that combines consistent hashing with forward probing to enforce strict load bounds.
• It rigorously proves that client movements are limited to O(log c/c) for c ≥ 2, ensuring system stability during dynamic updates.
• The approach has practical benefits for distributed systems, as demonstrated by its adoption in scalable cloud services like Google Cloud Pub/Sub.

Consistent Hashing with Bounded Loads: An Insightful Overview

The paper "Consistent Hashing with Bounded Loads" by Mirrokni, Thorup, and Zadimoghaddam addresses a significant issue in dynamic load balancing: the challenge of distributing clients (balls) across servers (bins) in a way that optimizes both the maximum load on any server and the number of movements required when the system is updated. Traditional solutions like Consistent Hashing and Rendezvous Hashing achieve load distribution comparable to random assignment, potentially leading to load imbalances. This paper proposes a hashing scheme that maintains specific load balancing criteria with minimal adjustments to bin assignments upon addition or removal of clients or servers.

Key Contributions and Technical Details

The authors propose a novel approach using a variant of Consistent Hashing augmented by linear probing to control load distribution more effectively. The method involves two key principles:

1. Hashing and Forwarding: Initially, clients and servers are hashed onto a unit circle, with each client landing in the bin immediately clockwise. If a bin exceeds its capacity, clients are forwarded to the nearest non-full bin. This approach helps in maintaining balance by ensuring no bin gets overloaded beyond a specified limit.
2. Capacity Constraints: The system introduces capacities for bins based on a user-specified parameter $c$. This balancing parameter ensures that no bin exceeds a load of $cm/n$, where $m$ is the number of clients and $n$ is the number of servers. The algorithm adapts dynamically, adjusting the assignment of clients as the system evolves, thus maintaining the balance in a fully distributed and efficient manner.

Theoretical Results

The authors provide rigorous proofs demonstrating that:

• When a client or server is added or removed, the expected number of client moves is $O(\log c/c)$ for $c \geq 2$ and $O(1/\epsilon^2)$ for $c = 1 + \epsilon \in (1, 2]$. These results ensure that the system remains stable, with minimal disruption during dynamic changes.
• The maximum load universally adheres to the constraint set by $c$, thereby addressing the core limitation of existing consistent hashing methods where load imbalance is pronounced for lightly loaded systems.

High Probability Bounds

The paper also offers high-probability bounds that hold for large client sets. These results indicate that, with overwhelming probability, the load on any server remains within $O((\log n)/c)$, providing further confidence in the applicability of the approach to large-scale systems where extreme load scenarios may occur due to the inherent randomness in hashing.

Practical Implications and Future Directions

This research has immediate practical implications, particularly in distributed systems and cloud environments where dynamic scalability is crucial. By enhancing the stability of hash-based load distribution, the approach can optimize resource utilization and minimize operational overhead. Empirical results presented in the paper support the theoretical findings, showing consistent adherence to expected load balances across a range of simulated configurations.

The method's simplicity and efficiency make it an attractive solution for implementing scalable distributed services. Its adoption within Google's Cloud Pub/Sub and similar applications at Vimeo underscores its practical utility. Looking forward, this work opens the door for further exploration into weighted client scenarios, even tighter high-probability bounds, and the extension to heterogeneous server capabilities, ensuring broader applicability across diverse computing environments.

In conclusion, this paper provides significant insights into improving load balancing in dynamic systems through advanced hashing techniques. Its blend of theoretical rigor and empirical validation offers a promising direction for future research in the efficient design and management of scalable distributed systems.