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Yayın On the maximum cardinality cut problem in proper interval graphs and related graph classes(Elsevier B.V., 2022-01-04) Boyacı, Arman; Ekim, Tınaz; Shalom, MordechaiAlthough it has been claimed in two different papers that the maximum cardinality cut problem is polynomial-time solvable for proper interval graphs, both of them turned out to be erroneous. In this work we consider the parameterized complexity of this problem. We show that the maximum cardinality cut problem in proper/unit interval graphs is FPT when parameterized by the maximum number of non-empty bubbles in a column of its bubble model. We then generalize this result to a more general graph class by defining new parameters related to the well-known clique-width parameter. Specifically, we define an (?,?,?)-clique-width decomposition of a graph as a clique-width decomposition in which at each step the following invariant is preserved: after discarding at most ? labels, a) every label consists of at most ? sets of twin vertices, and b) all the labels together induce a graph with independence number at most ?. We show that for every two constants ?,?>0 the problem is FPT when parameterized by ? plus the smallest width of an (?,?,?)-clique-width decomposition.Yayın On the online coalition structure generation problem(AI Access Foundationusc Information Sciences Inst, 2021) Flammini, Michele; Monaco, Gianpiero; Moscardelli, Luca; Shalom, Mordechai; Zaks, ShmuelWe consider the online version of the coalition structure generation problem, in which agents, corresponding to the vertices of a graph, appear in an online fashion and have to be partitioned into coalitions by an authority (i.e., an online algorithm). When an agent appears, the algorithm has to decide whether to put the agent into an existing coalition or to create a new one containing, at this moment, only her. The decision is irrevocable. The objective is partitioning agents into coalitions so as to maximize the resulting social welfare that is the sum of all coalition values. We consider two cases for the value of a coalition: (1) the sum of the weights of its edges, and (2) the sum of the weights of its edges divided by its size. Coalition structures appear in a variety of application in AI, multi-agent systems, networks, as well as in social networks, data analysis, computational biology, game theory, and scheduling. For each of the coalition value functions we consider the bounded and unbounded cases depending on whether or not the size of a coalition can exceed a given value alpha. Furthermore, we consider the case of a limited number of coalitions and various weight functions for the edges, i.e., unrestricted, positive and constant weights. We show tight or nearly tight bounds for the competitive ratio in each case.
