  Given an ordering of the vertices of a graph, the cost of covering an edge is
the smaller number of its two ends. The minimum sum vertex cover problem asks
for an ordering that minimizes the total cost of covering all edges. We
consider parameterized complexity of this problem, using the largest cost~$k$
of covering a single edge as the parameter. Note that the first $k$ vertices
form a (not necessarily minimal) vertex cover of the graph, and the ordering of
vertices after $k$ is irrelevant. We present a $(k^2 + 2 k)$-vertex kernel and
an $O(m + 2^kk! k^4)$-time algorithm for the minimum sum vertex cover problem,
where $m$ is the size of the input graph. Since our parameter~$k$ is
polynomially bounded by the vertex cover number of the input graph, our results
also apply to that parameterization.
