  During cancer progression, malignant cells accumulate somatic mutations that
can lead to genetic aberrations. In particular, evolutionary events akin to
segmental duplications or deletions can alter the copy-number profile (CNP) of
a set of genes in a genome. Our aim is to compute the evolutionary distance
between two cells for which only CNPs are known. This asks for the minimum
number of segmental amplifications and deletions to turn one CNP into another.
This was recently formalized into a model where each event is assumed to alter
a copy-number by $1$ or $-1$, even though these events can affect large
portions of a chromosome. We propose a general cost framework where an event
can modify the copy-number of a gene by larger amounts. We show that any cost
scheme that allows segmental deletions of arbitrary length makes computing the
distance strongly NP-hard. We then devise a factor $2$ approximation algorithm
for the problem when copy-numbers are non-zero and provide an implementation
called \textsf{cnp2cnp}. We evaluate our approach experimentally by
reconstructing simulated cancer phylogenies from the pairwise distances
inferred by \textsf{cnp2cnp} and compare it against two other alternatives,
namely the \textsf{MEDICC} distance and the Euclidean distance. The
experimental results show that our distance yields more accurate phylogenies on
average than these alternatives if the given CNPs are error-free, but that the
\textsf{MEDICC} distance is slightly more robust against error in the data. In
all cases, our experiments show that either our approach or the \textsf{MEDICC}
approach should preferred over the Euclidean distance.
