7,383 research outputs found
The Next 700 Impossibility Results in Time-Varying Graphs
We address highly dynamic distributed systems modeled by time-varying graphs
(TVGs). We interest in proof of impossibility results that often use informal
arguments about convergence. First, we provide a distance among TVGs to define
correctly the convergence of TVG sequences. Next, we provide a general
framework that formally proves the convergence of the sequence of executions of
any deterministic algorithm over TVGs of any convergent sequence of TVGs.
Finally, we illustrate the relevance of the above result by proving that no
deterministic algorithm exists to compute the underlying graph of any
connected-over-time TVG, i.e., any TVG of the weakest class of long-lived TVGs
The Next 700 Impossibility Results in Time-Varying Graphs
International audienceWe consider highly dynamic distributed systems modelled by time-varying graphs (TVGs). We first address proof of impossibility results that often use informal arguments about convergence. We provide a general framework that formally proves the convergence of the sequence of executions of any deterministic algorithm over TVGs of any convergent sequence of TVGs. Next, we focus of the weakest class of long-lived TVGs, i.e., the class of TVGs where any node can communicate any other node infinitely often. We illustrate the relevance of our result by showing that no deterministic algorithm is able to compute various distributed covering structure on any TVG of this class. Namely, our impossibility results focus on the eventual footprint, the minimal dominating set and the maximal matching problems
Gracefully Degrading Gathering in Dynamic Rings
Gracefully degrading algorithms [Biely \etal, TCS 2018] are designed to
circumvent impossibility results in dynamic systems by adapting themselves to
the dynamics. Indeed, such an algorithm solves a given problem under some
dynamics and, moreover, guarantees that a weaker (but related) problem is
solved under a higher dynamics under which the original problem is impossible
to solve. The underlying intuition is to solve the problem whenever possible
but to provide some kind of quality of service if the dynamics become
(unpredictably) higher.In this paper, we apply for the first time this approach
to robot networks. We focus on the fundamental problem of gathering a squad of
autonomous robots on an unknown location of a dynamic ring. In this goal, we
introduce a set of weaker variants of this problem. Motivated by a set of
impossibility results related to the dynamics of the ring, we propose a
gracefully degrading gathering algorithm
Robustness: a New Form of Heredity Motivated by Dynamic Networks
We investigate a special case of hereditary property in graphs, referred to
as {\em robustness}. A property (or structure) is called robust in a graph
if it is inherited by all the connected spanning subgraphs of . We motivate
this definition using two different settings of dynamic networks. The first
corresponds to networks of low dynamicity, where some links may be permanently
removed so long as the network remains connected. The second corresponds to
highly-dynamic networks, where communication links appear and disappear
arbitrarily often, subject only to the requirement that the entities are
temporally connected in a recurrent fashion ({\it i.e.} they can always reach
each other through temporal paths). Each context induces a different
interpretation of the notion of robustness.
We start by motivating the definition and discussing the two interpretations,
after what we consider the notion independently from its interpretation, taking
as our focus the robustness of {\em maximal independent sets} (MIS). A graph
may or may not admit a robust MIS. We characterize the set of graphs \forallMIS
in which {\em all} MISs are robust. Then, we turn our attention to the graphs
that {\em admit} a robust MIS (\existsMIS). This class has a more complex
structure; we give a partial characterization in terms of elementary graph
properties, then a complete characterization by means of a (polynomial time)
decision algorithm that accepts if and only if a robust MIS exists. This
algorithm can be adapted to construct such a solution if one exists
Scheduling trainees at a hospital department using a branch-and-price approach.
Scheduling trainees (graduate students) is a complicated problem that has to be solved frequently in many hospital departments. We will describe a trainee scheduling problem encountered in practice (at the ophthalmology department of the university hospital Gasthuisberg, Leuven). In this problem a department has a certain number of trainees at its disposal, which assist specialists in their activities (surgery, consultation, etc.). For each trainee one has to schedule the activities in which (s)he will assist during a certain time horizon, usually one year. Typically, these kind of scheduling problems are characterized by both hard and soft constraints. The hard constraints consist of both work covering constraints and formation requirements, whereas the soft constraints include trainees' preferences and setup restrictions. In this paper we will describe an exact branch-and-price method to solve the problem to optimality.Branch-and-price; Constraint; Health care; Problems; Requirements; Scheduling; Staff scheduling; Time; University;
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