Maximum matchings in random bipartite graphs and the space utilization of Cuckoo Hash tables

Frieze, Alan; Melsted, Páll

doi:10.1002/rsa.20427

Cited by 48 publications

(63 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(For now, we ignore the question of what algorithm finds such an assignment of keys to buckets -offline it can be turned into a maximum matching problem -and focus on the load threshold.) These thresholds have been determined [5], [7], [8], [9], [14].…”

Section: Cuckoo Hashingmentioning

confidence: 99%

“…This specific process finds the k-core of a hypergraph. The k-core itself appears in the analysis of several algorithms, and variations on this underlying process have arisen in the analysis of many problems that on their surface appear quite different, such as low-density paritycheck codes [16], cuckoo hashing [23], [5], [7], [9], and the satisfiability of random formulae [2], [18], [22].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Peeling arguments and double hashing

Mitzenmacher

Thaler

2012

2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

View full text Add to dashboard Cite

Abstract-The analysis of several algorithms and data structures can be reduced to the analysis of the following greedy "peeling" process: start with a random hypergraph; find a vertex of degree at most k, and remove it and all of its adjacent hyperedges from the graph; repeat until there is no suitable vertex. This specific process finds the k-core of a hypergraph, and variations on this theme have proven useful in analyzing for example decoding from low-density parity-check codes, several hash-based data structures such as cuckoo hashing, and algorithms for satisfiability of random formulae. This approach can be analyzed several ways, with two common approaches being via a corresponding branching process or a fluid limit family of differential equations.In this paper, we make note of an interesting aspect of these types of processes: the results are generally the same when the randomness is structured in the manner of double hashing. This phenomenon allows us to use less randomness and simplify the implementation for several hash-based data structures and algorithms. We explore this approach from both an empirical and theoretical perspective, examining theoretical justifications as well as simulation results for specific problems.

show abstract

Section: Cuckoo Hashingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Peeling arguments and double hashing

Mitzenmacher

Thaler

2012

2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

View full text Add to dashboard Cite

show abstract

“…For k = 2 several allocation algorithms and their analysis are closely connected to the cores of the associated graph. The s-core of a graph is the maximum vertex induced subgraph with minimum degree at least s. For instance Czumaj and Stemann [8] give a linear time algorithm achieving maximum load O(m/n) based on computation of all cores. Fernholz and Ramachandran [3] and Cain, Sanders, and Wormald [2] gave linear time algorithms for computing an optimal allocation (asymptotically almost surely).…”

Section: More Related Workmentioning

confidence: 99%

“…Is it possible to place each of the balls into one of their chosen bins such that each bin holds at most one ball? From [11,6,8] we know that there exists a critical size c * k n such that if m < c * k n then such an allocation is possible with high probability, otherwise this is not the case. In particular the following is known.…”

Section: Introductionmentioning

confidence: 99%

Balls into Bins Made Faster

Khosla

2013

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. Balls-into-bins games describe in an abstract setting several multiple-choice scenarios, and allow for a systematic and unified theoretical treatment. In the process that we consider, there are n bins, initially empty, and m = cn balls. Each ball chooses independently and uniformly at random k ≥ 3 bins. We are looking for an allocation such that each ball is placed into one of its chosen bins and no bin has load greater than 1. How quickly can we find such an allocation? We present a simple and novel algorithm that finds such an allocation (if it exists) and runs in linear time with high probability. Our algorithm finds applications in finding perfect matchings in a special class of sparse random bipartite graphs, orientation of random hypergraphs, load balancing and hashing.

show abstract

“…The random hypergraph case (

h \geq 2

) was studied by a few authors due to its applications in Cuckoo hashing and disk scheduling . See for

h \geq 2

and

k = 1

, and for

h \geq 2

and general

k

. A more general case where each ball can take

1 \leq w \leq h

copies and be assigned to

w

distinct bins was studied by the first author and Wormald for sufficiently large but constant

k

.…”

Section: Introductionmentioning

confidence: 99%

Arboricity and spanning‐tree packing in random graphs

Gao

Pérez‐Giménez

Sato

2017

Random Struct Algorithms

View full text Add to dashboard Cite

We study the arboricity A and the maximum number T of edge‐disjoint spanning trees of the classical random graph G(n,p). For all p(n)∈[0,1], we show that, with high probability, T is precisely the minimum of normalδ and true⌊m/(n−1)true⌋, where normalδ is the minimum degree of the graph and m denotes the number of edges. Moreover, we explicitly determine a sharp threshold value for p such that the following holds. Above this threshold, T equals true⌊m/(n−1)true⌋ and A equals true⌈m/(n−1)true⌉. Below this threshold, T equals normalδ, and we give a two‐value concentration result for the arboricity A in that range. Finally, we include a stronger version of these results in the context of the random graph process where the edges are randomly added one by one. A direct application of our result gives a sharp threshold for the maximum load being at most k in the two‐choice load balancing problem, where k→∞.

show abstract

Maximum matchings in random bipartite graphs and the space utilization of Cuckoo Hash tables

Cited by 48 publications

References 25 publications

Peeling arguments and double hashing

Peeling arguments and double hashing

Balls into Bins Made Faster

Arboricity and spanning‐tree packing in random graphs

Contact Info

Product

Resources

About