We investigate the manipulation of power indices in TU-cooperative games by stimulating (subject to a budget constraint) changes in the propensity of other players to participate to the game. We display several algorithms that show that the problem is often tractable for so-called network centrality games and influence attribution games, as well as an example when optimal manipulation is intractable, even though computing power indices is feasible.
First of all, (see e.g. @cite_25 @cite_36 ) is a well-established theme in combinatorial optimization. Our removal model can be seen as a special case of node interdiction.
@cite_36 @cite_25
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Given a directed graph G=(V,A) with a non-negative weight (length) function on its arcs w:A→ℝ+ and two terminals s,t∈V, our goal is to destroy all short directed paths from s to t in G by eliminating some arcs of A. This is known as the short paths interdiction problem. We consider several versions of it, and in each case analyze two subcases: total limited interdiction, when a fixed number k of arcs can be removed, and node-wise limited interdiction, when for each node v∈V a fixed number k(v) of out-going arcs can be removed. Our results indicate that the latter subcase is always easier than the former one. In particular, we show that the short paths node-wise interdiction problem can be efficiently solved by an extension of Dijkstra’s algorithm. In contrast, the short paths total interdiction problem is known to be NP-hard. We strengthen this hardness result by deriving the following inapproximability bounds: Given k, it is NP-hard to approximate within a factor c<2 the maximum s–t distance d(s,t) obtainable by removing (at most) k arcs from G. Furthermore, given d, it is NP-hard to approximate within a factor @math the minimum number of arcs which has to be removed to guarantee d(s,t)≥d. Finally, we also show that the same inapproximability bounds hold for undirected graphs and or node elimination. The problem of node overlap removal is to adjust the layout generated by typical graph drawing methods so that nodes of non-zero width and height do not overlap, yet are as close as possible to their original positions. We give an O(n log n) algorithm for achieving this assuming that the number of nodes overlapping any single node is bounded by some constant. This method has two parts, a constraint generation algorithm which generates a linear number of “separation” constraints and an algorithm for finding a solution to these constraints “close” to the original node placement values. We also extend our constraint solving algorithm to give an active set based algorithm which is guaranteed to find the optimal solution but which has considerably worse theoretical complexity. We compare our method with convex quadratic optimization and force scan approaches and find that it is faster than either, gives results of better quality than force scan methods and similar quality to the quadratic optimisation approach. We present an incomplete filtering algorithm for the circuit constraint. The filter removes redundant values by eliminating nonhamiltonian edges from the associated graph. We identify nonhamiltonian edges by analyzing a smaller graph with labeled edges that is defined on a separator of the original graph. The complexity of the procedure for each separator S is approximately O(|S|5). We found that it identified all infeasible instances and eliminated about one-third of the redundant domain elements in feasible instances. We present a novel method for key term extraction from text documents. In our method, document is modeled as a graph of semantic relationships between terms of that document. We exploit the following remarkable feature of the graph: the terms related to the main topics of the document tend to bunch up into densely interconnected subgraphs or communities, while non-important terms fall into weakly interconnected communities, or even become isolated vertices. We apply graph community detection techniques to partition the graph into thematically cohesive groups of terms. We introduce a criterion function to select groups that contain key terms discarding groups with unimportant terms. To weight terms and determine semantic relatedness between them we exploit information extracted from Wikipedia. Using such an approach gives us the following two advantages. First, it allows effectively processing multi-theme documents. Second, it is good at filtering out noise information in the document, such as, for example, navigational bars or headers in web pages. Evaluations of the method show that it outperforms existing methods producing key terms with higher precision and recall. Additional experiments on web pages prove that our method appears to be substantially more effective on noisy and multi-theme documents than existing methods.