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Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
On Computing the Maximum Parsimony Score of a Phylogenetic Network
Phylogenetic networks are used to display the relationship of different
species whose evolution is not treelike, which is the case, for instance, in
the presence of hybridization events or horizontal gene transfers. Tree
inference methods such as Maximum Parsimony need to be modified in order to be
applicable to networks. In this paper, we discuss two different definitions of
Maximum Parsimony on networks, "hardwired" and "softwired", and examine the
complexity of computing them given a network topology and a character. By
exploiting a link with the problem Multicut, we show that computing the
hardwired parsimony score for 2-state characters is polynomial-time solvable,
while for characters with more states this problem becomes NP-hard but is still
approximable and fixed parameter tractable in the parsimony score. On the other
hand we show that, for the softwired definition, obtaining even weak
approximation guarantees is already difficult for binary characters and
restricted network topologies, and fixed-parameter tractable algorithms in the
parsimony score are unlikely. On the positive side we show that computing the
softwired parsimony score is fixed-parameter tractable in the level of the
network, a natural parameter describing how tangled reticulate activity is in
the network. Finally, we show that both the hardwired and softwired parsimony
score can be computed efficiently using Integer Linear Programming. The
software has been made freely available
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