From Leiden to Pleasure Island: The Constant Potts Model for Community Detection as a Hedonic Game

Community detection is one of the fundamental problems in data science which consists of partitioning nodes into disjoint communities. We present a game-theoretic perspective on the Constant Potts Model (CPM) for partitioning networks into disjoint communities, emphasizing its efficiency, robustness, and accuracy. Efficiency: We reinterpret CPM as a potential hedonic game by decomposing its global Hamiltonian into local utility functions, where the local utility gain of each agent matches the corresponding increase in global utility. Leveraging this equivalence, we prove that local optimization of the CPM objective via better-response dynamics converges in pseudo-polynomial time to an equilibrium partition. Robustness: We introduce and relate two stability criteria: a strict criterion based on a novel notion of robustness, requiring nodes to simultaneously maximize neighbors and minimize non-neighbors within communities, and a relaxed utility function based on a weighted sum of these objectives, controlled by a resolution parameter. Accuracy: In community tracking scenarios, where initial partitions are used to bootstrap the Leiden algorithm with partial ground-truth information, our experiments reveal that robust partitions yield higher accuracy in recovering ground-truth communities.

Online Learning of Weakly Coupled MDP Policies for Load Balancing and Auto Scaling

Load balancing and auto scaling are at the core of scalable, contemporary systems, addressing dynamic resource allocation and service rate adjustments in response to workload changes. This paper introduces a novel model and algorithms for tuning load balancers coupled with auto scalers, considering bursty traffic arriving at finite queues. We begin by presenting the problem as a weakly coupled Markov Decision Processes (MDP), solvable via a linear program (LP). However, as the number of control variables of such LP grows combinatorially, we introduce a more tractable relaxed LP formulation, and extend it to tackle the problem of online parameter learning and policy optimization using a two-timescale algorithm based on the LP Lagrangian.