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Table 1 Results summary.

From: Multichromosomal median and halving problems under different genomic distances

problem context:
distance, #chr, linear, circular or mixed
distance halving double distance median guided halving
breakpoint unichr, circular or linear P open open NP [20, 21] open
breakpoint multichr, circular and mixed P new P new P new P new P new
breakpoint multichr, linear P new open P? P new NP new NP [27]
DCJ unichr, circular or linear P [3, 12] P [16] open NP [22] open
DCJ multichr, circular and mixed P [3, 12] P [4, 5] NP new NP new NP new
DCJ multichr, linear P [12] open open open NP? open NP?
RT unichr P [39] open open NP [22] open
RT multichr P [17, 3335] P [32] open NP? open NP? open NP?
  1. Status of complexity questions for five problems related to ancestral genome reconstruction, for eight genomic distances in the unichromosomal and multichromosomal contexts. Note that unichromosomal problems require that both input and output genomes be unichromosomal, so all problems involving doubled genomes are computationally defined in the circular case, when the doubled genome consists in a single circular chromosome composed of two successive occurences of the ordinary genome. Other versions of the halving problem are less restrictive [5, 16, 32]. P and NP stand for polynomial and NP-hard, respectively, and when followed by ?, represent our conjectures.