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**1 - 6**of**6**### Synchronizing clocks in the presence of . . .

, 1985

"... Algorithms are described for maintaining clock synchrony in a distributed multiprocess system where each process has its own clock. These algorithms work in the presence, of arbitrary clock or process failures, including “two-faced clocks” that present different values to different processes. Two of ..."

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Algorithms are described for maintaining clock synchrony in a distributed multiprocess system where each process has its own clock. These algorithms work in the presence, of arbitrary clock or process failures, including “two-faced clocks” that present different values to different processes. Two of the algorithms require that fewer than one-third of the processes be faulty. A third algorithm works if fewer than half the processes are faulty, but requires digital signatures.

### ON TIlE POSSIBILITY AND IMPOSSIBILITY OF ACHIEVING CLOCK SYNCHRONIZATION

"... ABSTRACT: It is known that clock synchronization can be achieved in the presence of faulty clocks numbering more than one-third of the total number of participating clocks provided that some authentication technique is used. Without authentication the number of faults that can be tolerated has been ..."

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ABSTRACT: It is known that clock synchronization can be achieved in the presence of faulty clocks numbering more than one-third of the total number of participating clocks provided that some authentication technique is used. Without authentication the number of faults that can be tolerated has been an open question. Here we show that if we restrict logical clocks to running within some linear function of real time, then clock synchronization is impossible, without au-thentication, when one-third or more of the processors are faulty. However, if there is a bound on the rate at which a processor can generate messages, then we show that clock synchronization is achievable, without authentication, as long as the faults do not disconnect the network. Finally, we provide a lower bound on the closeness to which simultaneity can be achieved in the network as a function of the transmis-sion and processing delay properties of the network. 1.

### unknown title

"... ABSTRACT: We analyze the problem of constructing a net-work which will have a fixed routing and which will be high-ly fault tolerant. A construction is presented which forms a "product route graph " from two or more constituent "route graphs. " The analysis involv ..."

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ABSTRACT: We analyze the problem of constructing a net-work which will have a fixed routing and which will be high-ly fault tolerant. A construction is presented which forms a &quot;product route graph &quot; from two or more constituent &quot;route graphs. &quot; The analysis involves the surviving route graph, which consists of all non-faulty nodes in the network with two nodes being connected by a directed edge iff the route from the first to the second is still intact after a set of component failures. The diameter of the surviving route graph, that is, the maximum distance between any pair of nodes, is a meas-ure of the worst-case performance degradation caused by the faults. The number of faults tolerated, the diameter, and the degree of the product graph are related in a simple way to the corresponding parameters of the constituent graphs. In addi-tion, there is a &quot;padding theorem &quot; which allows one to add

### Rigid Body Formation Control of a Multi-Agent Mobile ad hoc Wireless Network

, 2003

"... This paper presents an implementation of a symmetric distributed reduced order motion planning algorithm for formation control of mobile robots that uses middleware services to access information throughout a wireless ad hoc network. The implementation was tested on four MICAbots in a square formati ..."

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This paper presents an implementation of a symmetric distributed reduced order motion planning algorithm for formation control of mobile robots that uses middleware services to access information throughout a wireless ad hoc network. The implementation was tested on four MICAbots in a square formation. We demonstrate that the reduced order motion control algorithm can be used to control formations of nonholonomic mobile robots.

### FAULT-TOLERANT CLOCK SYNCHRONIZATION

"... Abstract: This paper gives two simple efficient dis-tributed algorithms: one for keeping clocks in a net-work synchronized and one for allowing new proc-essors to join the network with their clocks syn-chronized. The algorithms tolerate both link and node failures of any type. The algorithm for main ..."

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Abstract: This paper gives two simple efficient dis-tributed algorithms: one for keeping clocks in a net-work synchronized and one for allowing new proc-essors to join the network with their clocks syn-chronized. The algorithms tolerate both link and node failures of any type. The algorithm for main-taining synchronization will work for arbitrary net-works (rather than just completely connected net-works) and tolerates any number of processor or communication link faults as long as the correct processors remain connected by fault-free paths. It thus represents an improvement over other clock synchronization algorithms such as [LM1,LM2,LL1]. Our algorithm for allowing new processors to join requires that more than half the processors be cor-rect, a requirement which is provably necessary.