arXiv subjects

Quentin Bramas

Publications and source records attributed to Quentin Bramas.

20 records · Page 2Linked to original sources

arXiv2016

Packet Efficient Implementation of the Omega Failure Detector

We assume that a message may be delivered by packets through multiple hops and investigate the feasibility and efficiency of an implementation of the Omega Failure Detector under such an assumption.To motivate the study, we prove that the existence and sustainability of a leader is exponentially more probable in a multi-hop Omega implementation than in a single-hop one.An implementation is: \emph{message efficient} if all but finitely many messages are sent by a single process; \emph{packet efficient} if the number of packets used to transmit a message in all but finitely many messages is linear w.r.t the number of processes, packets of different messages may potentially use different channels, thus the number of used channels is not limited; \emph{super packet efficient} if the number of channels used by packets to transmit all but finitely many messages is linear.We present the following results for deterministic algorithms. If reliability and timeliness of one message does not correlate with another, i.e., there are no channel reliability properties, then a packet efficient implementation of Omega is impossible. If eventuallytimely and fair-lossy channels are considered, we establish necessary and sufficient conditions for the existence of a message and packet efficient implementation of Omega. We also prove that the eventuality of timeliness of channels makes a super packet efficientimplementation of Omega impossible. On the constructive side, we present and prove correct a deterministic packet efficient implementation of Omega that matches the necessary conditions we established.

cs.DC↗

arXiv2015

The Random Bit Complexity of Mobile Robots Scattering

We consider the problem of scattering $n$ robots in a two dimensional continuous space. As this problem is impossible to solve in a deterministic manner, all solutions must be probabilistic. We investigate the amount of randomness (that is, the number of random bits used by the robots) that is required to achieve scattering. We first prove that $n \log n$ random bits are necessary to scatter $n$ robots in any setting. Also, we give a sufficient condition for a scattering algorithm to be random bit optimal. As it turns out that previous solutions for scattering satisfy our condition, they are hence proved random bit optimal for the scattering problem. Then, we investigate the time complexity of scattering when strong multiplicity detection is not available. We prove that such algorithms cannot converge in constant time in the general case and in $o(\log \log n)$ rounds for random bits optimal scattering algorithms. However, we present a family of scattering algorithms that converge as fast as needed without using multiplicity detection. Also, we put forward a specific protocol of this family that is random bit optimal ($n \log n$ random bits are used) and time optimal ($\log \log n$ rounds are used). This improves the time complexity of previous results in the same setting by a $\log n$ factor. Aside from characterizing the random bit complexity of mobile robot scattering, our study also closes its time complexity gap with and without strong multiplicity detection (that is, $O(1)$ time complexity is only achievable when strong multiplicity detection is available, and it is possible to approach it as needed otherwise).

cs.DS↗