Contribution à l'algorithmique distribuée de contrôle : arbres couvrants avec et sans containtes
Résumé
In this PhD thesis, we present a study of distributed asynchronous
algorithms of control.
Distributed algorithms are algorithms operating on distributed
systems. These systems consist in networks of sites, where each site
can be either simple (when reduced to a single processor) or complex
(when expanded to a whole computer or a Local Area Network).
In this study, we only consider networks of sites sharing neither
memory nor global clock. Sites work in parallel, asynchronously and
each computation is only performed by message exchange. In such a
context, distributed algorithms are called ``message-driven''. We try
to limit waiting states by not introducing synchronization
mechanisms. Generally speaking, we make no particular assumption on
the way algorithms start, namely, any non-empty subset of sites may
start an algorithm. We try to remain as general as possible but in this
work, we limit our considerations to determinist algorithms. Our
assumptions are supporting the essential properties of distributed
algorithms~: that is essentially the local behaviour.
A control algorithm establishes a virtual structure over the whole
network in which each site can distinguish some of its neighbors to
play special roles. More particularly, we have chosen to study
structures which are similar to spanning trees. We recall that
numerous problems in distributed computing, such as distributed
termination and leader election, can be reduced to spanning tree
construction. In order to construct such a structure or to elect a
leader, most of known distributed algorithms transform this problem
into an extrema-finding problem. In fact, they elect the site which
has the greatest (or the lowest) identity and construct a spanning tree
at the same time.
We study two kinds of algorithms~: phase-based algorithms and
what we call anarchic algorithms. The latter algorithms are designed
to behave without any kind of synchronization. Of course their study
is difficult and they often need more message exchange, but this kind
of un-foreseeable behaviour is a rather good way for improving the fault tolerance.
We present a new algorithm of such a kind, moreover it is associated
to a leader election which is not an extrema-finding. Its analysis
leads us to show worst-case examples, but these examples are rare and our empirical average-case analysis show that this algorithm is almost as good as the best known algorithm for spanning tree construction.
This latter algorithm uses token-based methods and therefore behave more sequentially.
Other algorithms such as constructing constrained spanning trees, are
studied. The most popular constraint is the minimum total weight,
which represents an economical criterion. To our knowledge, the
Minimum Diameter Spanning Tree is a problem which had never been
addressed in the field of distributed research. We consider
``weighted'' diameter~: viz. the diameter $D$ of a graph is the sum of
the edges' weights along the longest shortest path. If we consider
time complexity, this constraint is obviously of great interest, since
it always exists a couple of sites needing at least $D$ units of time
to exchange information.
We present a method for constructing a MDST and from this method, we
give different algorithms, whether fault tolerance is needed or not.
Finally, the practical study of distributed algorithm on large
networks leads to build a simulator. Compared to the others
simulators, ours offer the advantage of being simple and easily
adaptable. In order to have faster and more realistic simulations, we
parallelize this algorithm. The same code can be performed on a
personal computer, a parallel computer or even a distributed machine.
algorithms of control.
Distributed algorithms are algorithms operating on distributed
systems. These systems consist in networks of sites, where each site
can be either simple (when reduced to a single processor) or complex
(when expanded to a whole computer or a Local Area Network).
In this study, we only consider networks of sites sharing neither
memory nor global clock. Sites work in parallel, asynchronously and
each computation is only performed by message exchange. In such a
context, distributed algorithms are called ``message-driven''. We try
to limit waiting states by not introducing synchronization
mechanisms. Generally speaking, we make no particular assumption on
the way algorithms start, namely, any non-empty subset of sites may
start an algorithm. We try to remain as general as possible but in this
work, we limit our considerations to determinist algorithms. Our
assumptions are supporting the essential properties of distributed
algorithms~: that is essentially the local behaviour.
A control algorithm establishes a virtual structure over the whole
network in which each site can distinguish some of its neighbors to
play special roles. More particularly, we have chosen to study
structures which are similar to spanning trees. We recall that
numerous problems in distributed computing, such as distributed
termination and leader election, can be reduced to spanning tree
construction. In order to construct such a structure or to elect a
leader, most of known distributed algorithms transform this problem
into an extrema-finding problem. In fact, they elect the site which
has the greatest (or the lowest) identity and construct a spanning tree
at the same time.
We study two kinds of algorithms~: phase-based algorithms and
what we call anarchic algorithms. The latter algorithms are designed
to behave without any kind of synchronization. Of course their study
is difficult and they often need more message exchange, but this kind
of un-foreseeable behaviour is a rather good way for improving the fault tolerance.
We present a new algorithm of such a kind, moreover it is associated
to a leader election which is not an extrema-finding. Its analysis
leads us to show worst-case examples, but these examples are rare and our empirical average-case analysis show that this algorithm is almost as good as the best known algorithm for spanning tree construction.
This latter algorithm uses token-based methods and therefore behave more sequentially.
Other algorithms such as constructing constrained spanning trees, are
studied. The most popular constraint is the minimum total weight,
which represents an economical criterion. To our knowledge, the
Minimum Diameter Spanning Tree is a problem which had never been
addressed in the field of distributed research. We consider
``weighted'' diameter~: viz. the diameter $D$ of a graph is the sum of
the edges' weights along the longest shortest path. If we consider
time complexity, this constraint is obviously of great interest, since
it always exists a couple of sites needing at least $D$ units of time
to exchange information.
We present a method for constructing a MDST and from this method, we
give different algorithms, whether fault tolerance is needed or not.
Finally, the practical study of distributed algorithm on large
networks leads to build a simulator. Compared to the others
simulators, ours offer the advantage of being simple and easily
adaptable. In order to have faster and more realistic simulations, we
parallelize this algorithm. The same code can be performed on a
personal computer, a parallel computer or even a distributed machine.
Nous présentons dans cette thèse une étude sur des
algorithmes distribués asynchrones et déterministes de
contröle. Un système distribué consiste en un réseau
de sites (processeurs, ordinateurs ou réseaux locaux). Dans cette
thèse, nous ne considérons que des réseaux de sites
communicants n'ayant ni mémoire partagée ni horloge globale.
De nombreux problèmes de l'algorithmique distribuée sont
réductibles à la construction d'un Arbre Couvrant qui est la
structure de contrôle qui nous intéresse.
Nous étudions deux types d'algorithmes~: ceux utilisant
la notion de phase logique et les autres qui ne considèrent aucun
mécanisme de synchronisation. Ces derniers ont des comportements
imprévisibles améliorant la tolérance aux fautes. Nous
présentons un nouvel algorithme de ce type associé à une
élection qui n'est pas une recherche d'extremum contrairement
à l'usage. Cet algorithme est comparable au meilleur
algorithme connu qui utilise des jetons et des phases logiques
induisant un comportement plus "séquentiel".
D'autres algorithmes, construisant des AC contraints, sont
considérés. En particulier l'AC de Diamètre Minimum qui
est, à notre connaissance, un problème qui n'a jamais
été étudié dans ce domaine. Le diamètre d'un
graphe est la somme des poids des arêtes du plus long des plus
courts chemins. Si nous considérons la complexité temporelle,
cette contrainte est d'un intérêt &vident. Nous proposons
différents algorithmes suivant que la tolérance aux fautes est
nécessaire ou non.
Finalement, l'étude pratique des algorithmes distribués sur
des réseaux de grande taille nous a conduit à la construction
d'un simulateur. Il permet l'exécution d'un même code source
sur des machines séquentielles ou parallèles.
algorithmes distribués asynchrones et déterministes de
contröle. Un système distribué consiste en un réseau
de sites (processeurs, ordinateurs ou réseaux locaux). Dans cette
thèse, nous ne considérons que des réseaux de sites
communicants n'ayant ni mémoire partagée ni horloge globale.
De nombreux problèmes de l'algorithmique distribuée sont
réductibles à la construction d'un Arbre Couvrant qui est la
structure de contrôle qui nous intéresse.
Nous étudions deux types d'algorithmes~: ceux utilisant
la notion de phase logique et les autres qui ne considèrent aucun
mécanisme de synchronisation. Ces derniers ont des comportements
imprévisibles améliorant la tolérance aux fautes. Nous
présentons un nouvel algorithme de ce type associé à une
élection qui n'est pas une recherche d'extremum contrairement
à l'usage. Cet algorithme est comparable au meilleur
algorithme connu qui utilise des jetons et des phases logiques
induisant un comportement plus "séquentiel".
D'autres algorithmes, construisant des AC contraints, sont
considérés. En particulier l'AC de Diamètre Minimum qui
est, à notre connaissance, un problème qui n'a jamais
été étudié dans ce domaine. Le diamètre d'un
graphe est la somme des poids des arêtes du plus long des plus
courts chemins. Si nous considérons la complexité temporelle,
cette contrainte est d'un intérêt &vident. Nous proposons
différents algorithmes suivant que la tolérance aux fautes est
nécessaire ou non.
Finalement, l'étude pratique des algorithmes distribués sur
des réseaux de grande taille nous a conduit à la construction
d'un simulateur. Il permet l'exécution d'un même code source
sur des machines séquentielles ou parallèles.