Matthew S. Levine

Consistent hashing and random trees: distributed caching protocols for relieving hot spots on the World Wide Web

We describe a family of caching protocols for distrib-uted networks that can be used to decrease or eliminate the occurrence of hot spots in the network. Our protocols are particularly designed for use with very large networks such as the Internet, where delays caused by hot spots can be severe, and where it is not feasible for every server to have complete information about the current state of the entire network. The protocols are easy to implement using existing network protocols such as TCP/IP, and require very little overhead. The protocols work with local control, make efficient use of existing resources, and scale gracefully as the network grows. Our caching protocols are based on a special kind of hashing that we call consistent hashing. Roughly speaking, a consistent hash function is one which changes minimally as the range of the function changes. Through the development of good consistent hash functions, we are able to develop caching protocols which do not require users to have a current or even consistent view of the network. We believe that consistent hash functions may eventually prove to be useful in other applications such as distributed name servers and/or quorum systems.

Finding maximum flows in undirected graphs seems easier than bipartite matching

Consider an n-vertex, m-edge, undirected graph with maximum flow value v. We give a method to find augmenting paths in such a graph in amortized sub-linear (O(npv)) time per path. This lets us improve the time bound of the classic augmenting path algorithm to O(m+ nv3=2) on simple graphs. The addition of a blocking flow subroutine gives a simple, deterministic O(nm2=3v1=6)-time algorithm. We also use our technique to improve known randomized algorithms, giving O(m+nv5=4)-time and O(m+n11=9v)-time algorithms for capacitated undirected graphs. For simple graphs, in which v n, the last bound is O(n2:2), improving on the best previous bound of O(n2:5), which is also the best known time bound for bipartite matching.

Random sampling in residual graphs

Consider an <i>n</i>-vertex, <i>m</i>-edge, undirected graph with maximum flow value <i>v</i>. We give a new <i>Õ</i>(<i>m+nv</i>)-time maximum flow algorithm based on finding augmenting paths in random samples of the edges of residual graphs. After assigning certain special sampling probabilities to edges in <i>Õ</i>(<i>m</i>) time, our algorithm is very simple: repeatedly find an augmenting path in a random sample of edges from the residual graph.

Finding the right cutting planes for the TSP

Given an instance of the Traveling Salesman Problem (TSP), a reasonable way to get a lower bound on the optimal answer is to solve a linear programming relaxation of an integer programming formulation of the problem. These linear programs typically have an exponential number of constraints, but in theory they can be solved efficiently with the ellipsoid method as long as we have an algorithm that can take a solution and either declare it feasible or find a violated constraint. In practice, it is often the case that many constraints are violated, which raises the question of how to choose among them so as to improve performance. For the simplest TSP formulation it is possible to efficiently find all the violated constraints, which gives us a good chance to try to answer this question empirically. Looking at random two dimensional Euclidean instances and the large instances from TSPLIB, we ran experiments to evaluate several strategies for picking among the violated constraints. We found some information about which constraints to prefer, which resulted in modest gains, but were unable to get large improvements in performance.

Fast Augmenting Paths by Random Sampling from Residual Graphs

Consider an

Finding the Right Cutting Planes for the TSP

n

Global load balancing across mirrored data centers

-vertex,

Method and apparatus for distributing requests among a plurality of resources

m

Method for extending a network map

-edge, undirected graph with integral capacities and max-flow value

Network performance monitoring in a content delivery system

v