A hundred impossibility proofs for distributed computing
Proceedings of the eighth annual ACM Symposium on Principles of distributed computing
Converting high probability into nearly-constant time—with applications to parallel hashing
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Fast and reliable parallel hashing
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Locality in distributed graph algorithms
SIAM Journal on Computing
Parallel randomized load balancing
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Exploiting storage redundancy to speed up randomized shared memory simulations
Theoretical Computer Science
Proceedings of the eighth annual ACM symposium on Parallel algorithms and architectures
The Tree Model for Hashing: Lower and Upper Bounds
SIAM Journal on Computing
On the analysis of randomized load balancing schemes
Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures
Allocating weighted jobs in parallel
Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures
Balls and bins: a study in negative dependence
Random Structures & Algorithms
Expected Length of the Longest Probe Sequence in Hash Code Searching
Journal of the ACM (JACM)
SIAM Journal on Computing
Randomized allocation processes
Random Structures & Algorithms
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
The Power of Collision: Randomized Parallel Algorithms for Chaining and Integer Sorting
Proceedings of the Tenth Conference on Foundations of Software Technology and Theoretical Computer Science
How asymmetry helps load balancing
Journal of the ACM (JACM)
Load balancing in the L/sub p/ norm
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
A Near-Tight Lower Bound on the Time Complexity of Distributed MST Construction
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The power of two choices in randomized load balancing
The power of two choices in randomized load balancing
Hundreds of impossibility results for distributed computing
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Balanced allocations with heterogenous bins
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Balanced allocations: the weighted case
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Distributed Selfish Load Balancing
SIAM Journal on Computing
Fast Distributed Approximations in Planar Graphs
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Leveraging Linial's Locality Limit
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
On weighted balls-into-bins games
Theoretical Computer Science
Load balancing without regret in the bulletin board model
Proceedings of the 28th ACM symposium on Principles of distributed computing
Parallel Randomized Load Balancing: A Lower Bound for a More General Model
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
The (1 + β)-choice process and weighted balls-into-bins
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Revisiting randomized parallel load balancing algorithms
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
The round complexity of distributed sorting: extended abstract
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Self-stabilizing local k-placement of replicas with minimal variance
SSS'12 Proceedings of the 14th international conference on Stabilization, Safety, and Security of Distributed Systems
"Tri, tri again": finding triangles and small subgraphs in a distributed setting
DISC'12 Proceedings of the 26th international conference on Distributed Computing
Optimal deterministic routing and sorting on the congested clique
Proceedings of the 2013 ACM symposium on Principles of distributed computing
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We explore the fundamental limits of distributed balls-into-bins algorithms, i.e., algorithms where balls act in parallel, as separate agents. This problem was introduced by Adler et al., who showed that non-adaptive and symmetric algorithms cannot reliably perform better than a maximum bin load of Theta(log log n / log log log n) within the same number of rounds. We present an adaptive symmetric algorithm that achieves a bin load of two in log* n+O(1) communication rounds using O(n) messages in total. Moreover, larger bin loads can be traded in for smaller time complexities. We prove a matching lower bound of (1-o(1))log* n on the time complexity of symmetric algorithms that guarantee small bin loads at an asymptotically optimal message complexity of O(n). The essential preconditions of the proof are (i) a limit of O(n) on the total number of messages sent by the algorithm and (ii) anonymity of bins, i.e., the port numberings of balls are not globally consistent. In order to show that our technique yields indeed tight bounds, we provide for each assumption an algorithm violating it, in turn achieving a constant maximum bin load in constant time. As an application, we consider the following problem. Given a fully connected graph of n nodes, where each node needs to send and receive up to n messages, and in each round each node may send one message over each link, deliver all messages as quickly as possible to their destinations. We give a simple and robust algorithm of time complexity O(log* n) for this task and provide a generalization to the case where all nodes initially hold arbitrary sets of messages. Completing the picture, we give a less practical, but asymptotically optimal algorithm terminating within O(1) rounds. All these bounds hold with high probability.