Weighted voting games are important in multiagent systems because of their usage in automated decision making. However, they are not immune from the vulnerability of false-name manipulation by strategic agents that may be present in the games. False-name manipulation involves an agent splitting its weight among several false identities in anticipation of power increase. Previous works have considered false-name manipulation using the well-known Shapley-Shubik and Banzhaf power indices. Bounds on the extent of power that a manipulator may gain exist when it splits into k D 2 false identities for both the Shapley-Shubik and Banzhaf indices. The bounds when an agent splits into k > 2 false identities, until now, have remained open for the two indices. This article answers this open problem by providing four nontrivial bounds when an agent splits into k > 2 false identities for the two indices. Furthermore, we propose a new bound on the extent of power that a manipulator may gain when it splits into several false identities in a class of games referred to as excess unanimity weighted voting games. Finally, we complement our theoretical results with empirical evaluation. Results from our experiments confirm the existence of beneficial splits into several false identities for the two indices, and also establish that splitting into more than two false identities is qualitatively different than the previously known splitting into exactly two false identities.
RNA secondary structure prediction is a fundamental problem in structural bioinformatics. The prediction problem is difficult because RNA secondary structures may contain pseudoknots formed by crossing base pairs. We introduce k-partite secondary structures as a simple classification of RNA secondary structures with pseudoknots. An RNA secondary structure is k-partite if it is the union of k pseudoknot-free sub-structures. Most known RNA secondary structures are either bipartite or tripartite. We show that there exists a constant number k such that any secondary structure can be modified into a k-partite secondary structure with approximately the same free energy. This offers a partial explanation of the prevalence of k-partite secondary structures with small k. We give a complete characterization of the computational complexities of recognizing k-partite secondary structures for all k ! 2, and show that this recognition problem is essentially the same as the k-colorability problem on circle graphs. We present two simple heuristics, iterated peeling and first-fit packing, for finding k-partite RNA secondary structures. For maximizing the number of base pair stackings, our iterated peeling heuristic achieves a constant approximation ratio of at most k for 2 k 5, and at most 6 1 À (1 À 6=k) k 6 1 À e À 6 56:01491 for k ! 6. Experiment on sequences from PseudoBase shows that our first-fit packing heuristic outperforms the leading method HotKnots in predicting RNA secondary structures with pseudoknots. Supplementary Material can be found at www.libertonline.com.
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