Utilitarian Welfare Optimization in the Generalized Vertex Coloring Games: An Implication to Venue Selection in Events Planning

We consider a general class of multi-agent games in networks, namely the generalized vertex coloring games (G-VCGs), inspired by real-life applications of the venue selection problem in events planning. Certain utility responding to the contemporary coloring assignment will be received by each agent under some particular mechanism, who, striving to maximize his own utility, is restricted to local information thus self-organizing when choosing another color. Our focus is on maximizing some utilitarian-looking welfare objective function concerning the cumulative utilities across the network in a decentralized fashion. Firstly, we investigate on a special class of the G-VCGs, namely Identical Preference VCGs (IP-VCGs) which recovers the rudimentary work by \cite{chaudhuri2008network}. We reveal its convergence even under a completely greedy policy and completely synchronous settings, with a stochastic bound on the converging rate provided. Secondly, regarding the general G-VCGs, a greediness-preserved Metropolis-Hasting based policy is proposed for each agent to initiate with the limited information and its optimality under asynchronous settings is proved using theories from the regular perturbed Markov processes. The policy was also empirically witnessed to be robust under independently synchronous settings. Thirdly, in the spirit of ``robust coloring'', we include an expected loss term in our objective function to balance between the utilities and robustness. An optimal coloring for this robust welfare optimization would be derived through a second-stage MH-policy driven algorithm. Simulation experiments are given to showcase the efficiency of our proposed strategy.Comment: 35 Page

Overlapping and Robust Edge-Colored Clustering in Hypergraphs

A recent trend in data mining has explored (hyper)graph clustering algorithms for data with categorical relationship types. Such algorithms have applications in the analysis of social, co-authorship, and protein interaction networks, to name a few. Many such applications naturally have some overlap between clusters, a nuance which is missing from current combinatorial models. Additionally, existing models lack a mechanism for handling noise in datasets. We address these concerns by generalizing Edge-Colored Clustering, a recent framework for categorical clustering of hypergraphs. Our generalizations allow for a budgeted number of either (a) overlapping cluster assignments or (b) node deletions. For each new model we present a greedy algorithm which approximately minimizes an edge mistake objective, as well as bicriteria approximations where the second approximation factor is on the budget. Additionally, we address the parameterized complexity of each problem, providing FPT algorithms and hardness results