Section: New Results
Network and Graph Algorithms
Vertex Coloring with Communication and Local Memory Constraints in Synchronous Broadcast Networks
Participants : Hicham Lakhlef, Michel Raynal, Francois Taiani.
This work [41] considers the broadcast/receive communication model in which
message collisions and message conflicts can occur because processes
share frequency bands. (A collision occurs when,
during the same round, messages are sent to the same process by too many
neighbors. A conflict occurs when a process and one of its neighbors
broadcast during the same round.) More precisely,
this work considers the case where, during a round, a process may
either broadcast a message to its neighbors or receive a message from
at most
Optimal Collision/Conflict-Free Distance-2 Coloring in Wireless Synchronous Broadcast/Receive Tree Networks
Participants : Davide Frey, Hicham Lakhlef, Michel Raynal.
We studied the problem of decentralized distance-2 coloring in
message-passing systems where communication is (a) synchronous and (b)
based on the “broadcast/receive” pair of communication
operations. “Synchronous” means that time is discrete and appears as a
sequence of time slots (or rounds) such that each message is received
in the very same round in which it is sent. “Broadcast/receive” means
that during a round a process can either broadcast a message to its
neighbors or receive a message from one of them. In such a
communication model, no two neighbors of the same process, nor a
process and any of its neighbors, must be allowed to broadcast during
the same time slot (thereby preventing message collisions in the first
case, and message conflicts in the second case). From a graph theory
point of view, the allocation of slots to processes is know as the
distance-2 coloring problem: a color must be associated with each
process (defining the time slots in which it will be allowed to
broadcast) in such a way that any two processes at distance at most 2
obtain different colors, while the total number of colors is “as small
as possible”. In this context, we proposed a parallel message-passing
distance-2 coloring algorithm suited to trees, whose roots are
dynamically defined. This algorithm, which is itself collision-free
and conflict-free, uses
Efficient Plurality Consensus, or: The Benefits of Cleaning Up from Time to Time
Participant : George Giakkoupis.
Plurality consensus considers a network of
In [22], we propose two protocols that need only mild assumptions on the bias in favor of the plurality.
As an example of our results, consider the complete graph and an arbitrarily small constant multiplicative bias in favor of the plurality.
Our first protocol achieves plurality consensus in
This work was done in collaboration with Petra Berenbrink (SFU), Tom Friedetzky (Durham University), and Peter Kling (SFU).
Bounds on the Voter Model in Dynamic Networks
Participants : George Giakkoupis, Anne-Marie Kermarrec.
In the voter model, each node of a graph has an opinion, and in every round each node chooses independently a random neighbour and adopts its opinion. We are interested in the consensus time, which is the first point in time where all nodes have the same opinion.
In [23], we consider dynamic graphs
in which the edges are rewired in every round (by an adversary) giving rise to the graph sequence
This work was done in collaboration with Petra Berenbrink (SFU), and Frederik Mallmann-Trenn (SFU).
How Asynchrony Affects Rumor Spreading Time
Participant : George Giakkoupis.
In standard randomized (push-pull) rumor spreading, nodes communicate in synchronized rounds. In each round every node contacts a random neighbor in order to exchange the rumor (i.e., either push the rumor to its neighbor or pull it from the neighbor). A natural asynchronous variant of this algorithm is one where each node has an independent Poisson clock with rate 1, and every node contacts a random neighbor whenever its clock ticks. This asynchronous variant is arguably a more realistic model in various settings, including message broadcasting in communication networks, and information dissemination in social networks.
In [35] we study how asynchrony affects the rumor spreading time, that is, the time before a rumor originated at a single node spreads to all nodes in the graph. Our first result states that the asynchronous push-pull rumor spreading time is asymptotically bounded by the standard synchronous time. Precisely, we show that for any graph
These results improve upon the bounds for both directions shown recently by Acan et al. (PODC 2015). An interesting implication of our first result is that in regular graphs, the weaker push-only variant of synchronous rumor spreading has the same asymptotic performance as the synchronous push-pull algorithm.
This work was done in collaboration with Yasamin Nazari and Philipp Woelfel from the University of Calgary.
Amplifiers and Suppressors of Selection for the Moran Process on Undirected Graphs
Participant : George Giakkoupis.
In [47] we consider the classic Moran process modeling the spread of genetic mutations, as extended to structured populations by Lieberman et al. (Nature, 2005).
In this process, individuals are the vertices of a connected graph
A problem that has received significant attention recently concerns the existence of families of graphs, called strong amplifiers of selection, for which the fixation probability tends to 1 as the order