32,801 research outputs found
Finite-time Convergent Gossiping
Gossip algorithms are widely used in modern distributed systems, with
applications ranging from sensor networks and peer-to-peer networks to mobile
vehicle networks and social networks. A tremendous research effort has been
devoted to analyzing and improving the asymptotic rate of convergence for
gossip algorithms. In this work we study finite-time convergence of
deterministic gossiping. We show that there exists a symmetric gossip algorithm
that converges in finite time if and only if the number of network nodes is a
power of two, while there always exists an asymmetric gossip algorithm with
finite-time convergence, independent of the number of nodes. For nodes,
we prove that a fastest convergence can be reached in node
updates via symmetric gossiping. On the other hand, under asymmetric gossip
among nodes with , it takes at least node
updates for achieving finite-time convergence. It is also shown that the
existence of finite-time convergent gossiping often imposes strong structural
requirements on the underlying interaction graph. Finally, we apply our results
to gossip algorithms in quantum networks, where the goal is to control the
state of a quantum system via pairwise interactions. We show that finite-time
convergence is never possible for such systems.Comment: IEEE/ACM Transactions on Networking, In Pres
Limit points of the monotonic schemes
Many numerical simulations in quantum (bilinear) control use the
monotonically convergent algorithms of Krotov (introduced by Tannor), Zhu &
Rabitz or the general form of Maday & Turinici. This paper presents an analysis
of the limit set of controls provided by these algorithms and a proof of
convergence in a particular case.Comment: 5 pages, 0 figure, 44th IEEE conference on Decision and Control
Sevilla december 200
An Algorithmic Framework for Strategic Fair Division
We study the paradigmatic fair division problem of allocating a divisible
good among agents with heterogeneous preferences, commonly known as cake
cutting. Classical cake cutting protocols are susceptible to manipulation. Do
their strategic outcomes still guarantee fairness?
To address this question we adopt a novel algorithmic approach, by designing
a concrete computational framework for fair division---the class of Generalized
Cut and Choose (GCC) protocols}---and reasoning about the game-theoretic
properties of algorithms that operate in this model. The class of GCC protocols
includes the most important discrete cake cutting protocols, and turns out to
be compatible with the study of fair division among strategic agents. In
particular, GCC protocols are guaranteed to have approximate subgame perfect
Nash equilibria, or even exact equilibria if the protocol's tie-breaking rule
is flexible. We further observe that the (approximate) equilibria of
proportional GCC protocols---which guarantee each of the agents a
-fraction of the cake---must be (approximately) proportional. Finally, we
design a protocol in this framework with the property that its Nash equilibrium
allocations coincide with the set of (contiguous) envy-free allocations
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