14 research outputs found
On Coloring Resilient Graphs
We introduce a new notion of resilience for constraint satisfaction problems,
with the goal of more precisely determining the boundary between NP-hardness
and the existence of efficient algorithms for resilient instances. In
particular, we study -resiliently -colorable graphs, which are those
-colorable graphs that remain -colorable even after the addition of any
new edges. We prove lower bounds on the NP-hardness of coloring resiliently
colorable graphs, and provide an algorithm that colors sufficiently resilient
graphs. We also analyze the corresponding notion of resilience for -SAT.
This notion of resilience suggests an array of open questions for graph
coloring and other combinatorial problems.Comment: Appearing in MFCS 201
Coalition Resilient Outcomes in Max k-Cut Games
We investigate strong Nash equilibria in the \emph{max -cut game}, where
we are given an undirected edge-weighted graph together with a set of colors. Nodes represent players and edges capture their mutual
interests. The strategy set of each player consists of the colors. When
players select a color they induce a -coloring or simply a coloring. Given a
coloring, the \emph{utility} (or \emph{payoff}) of a player is the sum of
the weights of the edges incident to , such that the color chosen
by is different from the one chosen by . Such games form some of the
basic payoff structures in game theory, model lots of real-world scenarios with
selfish agents and extend or are related to several fundamental classes of
games.
Very little is known about the existence of strong equilibria in max -cut
games. In this paper we make some steps forward in the comprehension of it. We
first show that improving deviations performed by minimal coalitions can cycle,
and thus answering negatively the open problem proposed in
\cite{DBLP:conf/tamc/GourvesM10}. Next, we turn our attention to unweighted
graphs. We first show that any optimal coloring is a 5-SE in this case. Then,
we introduce -local strong equilibria, namely colorings that are resilient
to deviations by coalitions such that the maximum distance between every pair
of nodes in the coalition is at most . We prove that -local strong
equilibria always exist. Finally, we show the existence of strong Nash
equilibria in several interesting specific scenarios.Comment: A preliminary version of this paper will appear in the proceedings of
the 45th International Conference on Current Trends in Theory and Practice of
Computer Science (SOFSEM'19
Courtesy as a Means to Coordinate
We investigate the problem of multi-agent coordination under rationality
constraints. Specifically, role allocation, task assignment, resource
allocation, etc. Inspired by human behavior, we propose a framework (CA^3NONY)
that enables fast convergence to efficient and fair allocations based on a
simple convention of courtesy. We prove that following such convention induces
a strategy which constitutes an -subgame-perfect equilibrium of the
repeated allocation game with discounting. Simulation results highlight the
effectiveness of CA^3NONY as compared to state-of-the-art bandit algorithms,
since it achieves more than two orders of magnitude faster convergence, higher
efficiency, fairness, and average payoff.Comment: Accepted at AAMAS 2019 (International Conference on Autonomous Agents
and Multiagent Systems
Stabilization Bounds for Influence Propagation from a Random Initial State
We study the stabilization time of two common types of influence propagation.
In majority processes, nodes in a graph want to switch to the most frequent
state in their neighborhood, while in minority processes, nodes want to switch
to the least frequent state in their neighborhood. We consider the sequential
model of these processes, and assume that every node starts out from a uniform
random state.
We first show that if nodes change their state for any small improvement in
the process, then stabilization can last for up to steps in both
cases. Furthermore, we also study the proportional switching case, when nodes
only decide to change their state if they are in conflict with a
fraction of their neighbors, for some parameter . In this case, we show that if , then there
is a construction where stabilization can indeed last for
steps for some constant . On the other hand, if ,
we prove that the stabilization time of the processes is upper-bounded by
Stabilization Time in Weighted Minority Processes
A minority process in a weighted graph is a dynamically changing coloring.
Each node repeatedly changes its color in order to minimize the sum of weighted
conflicts with its neighbors. We study the number of steps until such a process
stabilizes. Our main contribution is an exponential lower bound on
stabilization time. We first present a construction showing this bound in the
adversarial sequential model, and then we show how to extend the construction
to establish the same bound in the benevolent sequential model, as well as in
any reasonable concurrent model. Furthermore, we show that the stabilization
time of our construction remains exponential even for very strict switching
conditions, namely, if a node only changes color when almost all (i.e., any
specific fraction) of its neighbors have the same color. Our lower bound works
in a wide range of settings, both for node-weighted and edge-weighted graphs,
or if we restrict minority processes to the class of sparse graphs