2 research outputs found
Approximate Majority with Catalytic Inputs
Population protocols are a class of algorithms for modeling distributed
computation in networks of finite-state agents communicating through pairwise
interactions. Their suitability for analyzing numerous chemical processes has
motivated the adaptation of the original population protocol framework to
better model these chemical systems. In this paper, we further the study of two
such adaptations in the context of solving approximate majority:
persistent-state agents (or catalysts) and spontaneous state changes (or
leaks).
Based on models considered in recent protocols for populations with
persistent-state agents, we assume a population with catalytic input agents
and worker agents, and the goal of the worker agents is to compute some
predicate over the states of the catalytic inputs. We call this model the
Catalytic Input (CI) model. For , we show that computing the
parity of the input population with high probability requires at least
total interactions, demonstrating a strong separation between the
CI model and the standard population protocol model. On the other hand, we show
that the simple third-state dynamics of Angluin et al. for approximate majority
in the standard model can be naturally adapted to the CI model: we present such
a constant-state protocol for the CI model that solves approximate majority in
total steps with high probability when the input margin is
.
We then show the robustness of third-state dynamics protocols to the
transient leaks events introduced by Alistarh et al. In both the original and
CI models, these protocols successfully compute approximate majority with high
probability in the presence of leaks occurring at each step with probability
, exhibiting a resilience to leaks
similar to that of Byzantine agents in previous works
Stable routing scheduling algorithms in multi-hop wireless networks
Stability is an important issue in order to characterize the performance of a network, and it has become a major topic of study in the last decade. Roughly speaking, a communication network system is said to be stableif the number of packets waiting to be delivered (backlog) is finitely bounded at any one time.
In this paper we introduce a number of routing scheduling algorithms which, making use of certain knowledge about the network’s structure, guarantee stability for certain injection rates.
First, we introduce two new families of combinatorial structures, which we call universally strong selectorsand generalized universally strong selectors, that are used to provide a set of transmission schedules. Making use of these structures, we propose two local-knowledgepacket-oblivious routing scheduling algorithms. The first proposed routing scheduling algorithm onlyneeds to know some upper bounds on the number of links and on the network’s degree, and is asymptotically optimal regarding the injection rate for which stability is guaranteed. The second proposed routing scheduling algorithm isclose to be asymptotically optimal, but it only needs to know an upper bound on the number of links. For such algorithms, we also provide some results regarding both the maximum latencies and queue lengths. Furthermore, we also evaluate how the lack of global knowledge about the system topology affects the performance of the routing scheduling algorithms.Funding for open access charge: CRUE-Universitat Jaume