Darin Goldstein

On the Complexity of Network Synchronization

We show that if a minimal-time solution to a fundamental distributed computation primitive, synchronizing a network path of finite-state processors, exists on the three-dimensional, undirected grid, then we can conclude the purely complexity-theoretic result

On formulations of firing squad synchronization problems

P = NP

Can memory be used adaptively by uniform algorithms

. Every previous result on network synchronization for various network topologies either demonstrates the existence of fast synchronization solutions or proves that a synchronization solution cannot exist at all. To date, it is unknown whether there is a network topology for which there exists a synchronization solution but for which no minimal-time synchronization solution exists. Under the assumption that

On the complexity of network synchronization

P \neq NP

On Minimal-Time Solutions of Firing Squad Synchronization Problems for Networks

, this paper solves this longstanding open problem in the affirmative.

On the complexity of the “most general” firing squad synchronization problem

We propose a novel formulation of the firing squad synchronization problem. In this formulation we may use more than one general state and the general state to be used is determined by the boundary condition of the general. We show that the usual formulation and the new formulation yield different minimum firing times for some variations of the problem. Our results suggest that the new formulation is more suited for the general theory of the firing squad synchronization problem.

A "Go With the Winners" approach to finding frequent patterns

We introduce a novel term, memory-adaptive, that intuitively captures what it means for a distributed protocol to most efficiently make use of its shared memory. We also prove three results that relate to our memory-adaptive model. In our store/release protocols processors are required to store a value in shared MWMR memory so that it cannot be overwritten until it has been released by the processor. We show that there do not exist uniformly wait-free store/release protocols using only the basic operations read and write that are memory-adaptive to point contention. We further show that there exists a uniformly wait-free store/release protocol using only the basic operations read and write that is memory-adaptive to total contention. We finally show that there exists a uniformly wait-free store/release protocol using only the basic operations read, write, and write-plus that is memory-adaptive to interval contention and time-adaptive to total contention.

On the Formulation and Solution of the Convoy Routing Problem

We show that if a minimal-time solution to a fundamental distributed computation primitive, synchronizing a network path of finite-state processors, exists on the three-dimensional, undirected grid, then we can conclude the purely complexity-theoretic result P=NP. Every previous result on network synchronization for various network topologies either demonstrates the existence of fast synchronization solutions or proves that a synchronization solution cannot exist at all To date, it is unknown whether there is a network topology for which there exists a synchronization solution but for which no minimal-time synchronization solution exists Under the assumption that P ≠ NP, this paper solves this longstanding open problem in the affirmative.

Determination of the topology of a directed network

The goal of this work is to show that if a minimal-time solution exists for a fundamental computation primitive, synchronizing networks of finite-state processors (formally known as the firing squad synchronization problems for directed and undirected networks), then there must exist „extraordinarily fast” algorithms for exactly solving the diameter problem in the standard RAM model of computation. These results can therefore be interpreted either as evidence that such minimal-time solutions for synchronization do not exist or as a potentially major algorithmic leap forward in the study of the diameter problem. We conjecture that the former is true. These results essentially complete the program outlined in [K. Kobayashi, Theoret. Comput. Sci., 259 (2001), pp. 129--143] to show that there exist a wide range of natural topologies for which it seems highly unlikely that there exist minimal-time solutions.

On the complexity of the most general undirected firing squad synchronization problem

We show that if a minimal-time solution exists for a fundamental distributed computation primitive, synchronizing a general directed network of finite-state processors, then there must exist an extraordinarily fast