Rendezvous or highest random weight (HRW) hashing is an algorithm that allows clients to achieve distributed agreement on a set of k {\displaystyle k} options out of a possible set of n {\displaystyle n} options. A typical application is when clients need to agree on which sites (or proxies) objects are assigned to. Consistent hashing addresses the special case k = 1 {\displaystyle k=1} using a different method. Rendezvous hashing is both much simpler and more general than consistent hashing (see below). == History == Rendezvous hashing was invented by David Thaler and Chinya Ravishankar at the University of Michigan in 1996. Consistent hashing appeared a year later in the literature. Given its simplicity and generality, rendezvous hashing is now being preferred to consistent hashing in real-world applications. Rendezvous hashing was used very early on in many applications including mobile caching, router design, secure key establishment, and sharding and distributed databases. Other examples of real-world systems that use Rendezvous Hashing include the GitHub load balancer, the Apache Ignite distributed database, the Tahoe-LAFS file store, the CoBlitz large-file distribution service, Apache Druid, IBM's Cloud Object Store, the Arvados Data Management System, Apache Kafka, and the Twitter EventBus pub/sub platform. One of the first applications of rendezvous hashing was to enable multicast clients on the Internet (in contexts such as the MBONE) to identify multicast rendezvous points in a distributed fashion. It was used in 1998 by Microsoft's Cache Array Routing Protocol (CARP) for distributed cache coordination and routing. Some Protocol Independent Multicast routing protocols use rendezvous hashing to pick a rendezvous point. == Problem definition and approach == === Algorithm === Rendezvous hashing solves a general version of the distributed hash table problem: We are given a set of n {\displaystyle n} sites (servers or proxies, say). How can any set of clients, given an object O {\displaystyle O} , agree on a k-subset of sites to assign to O {\displaystyle O} ? The standard version of the problem uses k = 1. Each client is to make its selection independently, but all clients must end up picking the same subset of sites. This is non-trivial if we add a minimal disruption constraint, and require that when a site fails or is removed, only objects mapping to that site need be reassigned to other sites. The basic idea is to give each site S j {\displaystyle S_{j}} a score (a weight) for each object O i {\displaystyle O_{i}} , and assign the object to the highest scoring site. All clients first agree on a hash function h ( ⋅ ) {\displaystyle h(\cdot )} . For object O i {\displaystyle O_{i}} , the site S j {\displaystyle S_{j}} is defined to have weight w i , j = h ( O i , S j ) {\displaystyle w_{i,j}=h(O_{i},S_{j})} . Each client independently computes these weights w i , 1 , w i , 2 … w i , n {\displaystyle w_{i,1},w_{i,2}\dots w_{i,n}} and picks the k sites that yield the k largest hash values. The clients have thereby achieved distributed k {\displaystyle k} -agreement. If a site S {\displaystyle S} is added or removed, only the objects mapping to S {\displaystyle S} are remapped to different sites, satisfying the minimal disruption constraint above. The HRW assignment can be computed independently by any client, since it depends only on the identifiers for the set of sites S 1 , S 2 … S n {\displaystyle S_{1},S_{2}\dots S_{n}} and the object being assigned. HRW easily accommodates different capacities among sites. If site S k {\displaystyle S_{k}} has twice the capacity of the other sites, we simply represent S k {\displaystyle S_{k}} twice in the list, say, as S k , 1 , S k , 2 {\displaystyle S_{k,1},S_{k,2}} . Clearly, twice as many objects will now map to S k {\displaystyle S_{k}} as to the other sites. === Properties === Consider the simple version of the problem, with k = 1, where all clients are to agree on a single site for an object O. Approaching the problem naively, it might appear sufficient to treat the n sites as buckets in a hash table and hash the object name O into this table. Unfortunately, if any of the sites fails or is unreachable, the hash table size changes, forcing all objects to be remapped. This massive disruption makes such direct hashing unworkable. Under rendezvous hashing, however, clients handle site failures by picking the site that yields the next largest weight. Remapping is required only for objects currently mapped to the failed site, and disruption is minimal. Rendezvous hashing has the following properties: Low overhead: The hash function used is efficient, so overhead at the clients is very low. Load balancing: Since the hash function is randomizing, each of the n sites is equally likely to receive the object O. Loads are uniform across the sites. Site capacity: Sites with different capacities can be represented in the site list with multiplicity in proportion to capacity. A site with twice the capacity of the other sites will be represented twice in the list, while every other site is represented once. High hit rate: Since all clients agree on placing an object O into the same site SO, each fetch or placement of O into SO yields the maximum utility in terms of hit rate. The object O will always be found unless it is evicted by some replacement algorithm at SO. Minimal disruption: When a site fails, only the objects mapped to that site need to be remapped. Disruption is at the minimal possible level. Distributed k-agreement: Clients can reach distributed agreement on k sites simply by selecting the top k sites in the ordering. == O(log n) running time via skeleton-based hierarchical rendezvous hashing == The standard version of Rendezvous Hashing described above works quite well for moderate n, but when n {\displaystyle n} is extremely large, the hierarchical use of Rendezvous Hashing achieves O ( log n ) {\displaystyle O(\log n)} running time. This approach creates a virtual hierarchical structure (called a "skeleton"), and achieves O ( log n ) {\displaystyle O(\log n)} running time by applying HRW at each level while descending the hierarchy. The idea is to first choose some constant m {\displaystyle m} and organize the n {\displaystyle n} sites into c = ⌈ n / m ⌉ {\displaystyle c=\lceil n/m\rceil } clusters C 1 = { S 1 , S 2 … S m } , C 2 = { S m + 1 , S m + 2 … S 2 m } … {\displaystyle C_{1}=\left\{S_{1},S_{2}\dots S_{m}\right\},C_{2}=\left\{S_{m+1},S_{m+2}\dots S_{2m}\right\}\dots } Next, build a virtual hierarchy by choosing a constant f {\displaystyle f} and imagining these c {\displaystyle c} clusters placed at the leaves of a tree T {\displaystyle T} of virtual nodes, each with fanout f {\displaystyle f} . In the accompanying diagram, the cluster size is m = 4 {\displaystyle m=4} , and the skeleton fanout is f = 3 {\displaystyle f=3} . Assuming 108 sites (real nodes) for convenience, we get a three-tier virtual hierarchy. Since f = 3 {\displaystyle f=3} , each virtual node has a natural numbering in octal. Thus, the 27 virtual nodes at the lowest tier would be numbered 000 , 001 , 002 , . . . , 221 , 222 {\displaystyle 000,001,002,...,221,222} in octal (we can, of course, vary the fanout at each level - in that case, each node will be identified with the corresponding mixed-radix number). The easiest way to understand the virtual hierarchy is by starting at the top, and descending the virtual hierarchy. We successively apply Rendezvous Hashing to the set of virtual nodes at each level of the hierarchy, and descend the branch defined by the winning virtual node. We can in fact start at any level in the virtual hierarchy. Starting lower in the hierarchy requires more hashes, but may improve load distribution in the case of failures. For example, instead of applying HRW to all 108 real nodes in the diagram, we can first apply HRW to the 27 lowest-tier virtual nodes, selecting one. We then apply HRW to the four real nodes in its cluster, and choose the winning site. We only need 27 + 4 = 31 {\displaystyle 27+4=31} hashes, rather than 108. If we apply this method starting one level higher in the hierarchy, we would need 9 + 3 + 4 = 16 {\displaystyle 9+3+4=16} hashes to get to the winning site. The figure shows how, if we proceed starting from the root of the skeleton, we may successively choose the virtual nodes ( 2 ) 3 {\displaystyle (2)_{3}} , ( 20 ) 3 {\displaystyle (20)_{3}} , and ( 200 ) 3 {\displaystyle (200)_{3}} , and finally end up with site 74. The virtual hierarchy need not be stored, but can be created on demand, since the virtual nodes names are simply prefixes of base- f {\displaystyle f} (or mixed-radix) representations. We can easily create appropriately sorted strings from the digits, as required. In the example, we would be working with the strings 0 , 1 , 2 {\displaystyle 0,1,2} (at tier 1), 20 , 21 , 22 {\displaystyle 20,21,22} (at tier 2), and 200 , 201 , 202
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