850 research outputs found
When in Need, Nature is There for You:The Restorative Effects of Nature in Supporting the Prevention and Treatment of Mental Health Problems
Two cases of impact assessment in environmental lawmaking and the role of evidence in the European legislative process'
Agreement forests of caterpillar trees: complexity, kernelization and branching
Given a set of species, a phylogenetic tree is an unrooted binary tree
whose leaves are bijectively labelled by . Such trees can be used to show
the way species evolve over time. One way of understanding how topologically
different two phylogenetic trees are, is to construct a minimum-size agreement
forest: a partition of into the smallest number of blocks, such that the
blocks induce homeomorphic, non-overlapping subtrees in both trees. This
comparison yields insight into commonalities and differences in the evolution
of across the two trees. Computing a smallest agreement forest is NP-hard
(Hein, Jiang, Wang and Zhang, Discrete Applied Mathematics 71(1-3), 1996). In
this work we study the problem on caterpillars, which are path-like
phylogenetic trees. We will demonstrate that, even if we restrict the input to
this highly restricted subclass, the problem remains NP-hard and is in fact
APX-hard. Furthermore we show that for caterpillars two standard reductions
rules well known in the literature yield a tight kernel of size at most ,
compared to for general trees (Kelk and Simone, SIAM Journal on Discrete
Mathematics 33(3), 2019). Finally we demonstrate that we can determine if two
caterpillars have an agreement forest with at most blocks in
time, compared to for general trees (Chen, Fan and Sze, Theoretical
Computater Science 562, 2015), where suppresses polynomial factors.Comment: 31 pages, 15 figure
How the regulatory state differs. The constitutional dimensions of rulemaking in the European Union and the United States
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