  A $k$-page linear graph layout of a graph $G = (V,E)$ draws all vertices
along a line $\ell$ and each edge in one of $k$ disjoint halfplanes called
pages, which are bounded by $\ell$. We consider two types of pages. In a stack
page no two edges should cross and in a queue page no edge should be nested by
another edge. A crossing (nesting) in a stack (queue) page is called a
conflict. The algorithmic problem is twofold and requires to compute (i) a
vertex ordering and (ii) a page assignment of the edges such that the resulting
layout is either conflict-free or conflict-minimal. While linear layouts with
only stack or only queue pages are well-studied, mixed $s$-stack $q$-queue
layouts for $s,q \ge 1$ have received less attention. We show NP-completeness
results on the recognition problem of certain mixed linear layouts and present
a new heuristic for minimizing conflicts. In a computational experiment for the
case $s, q = 1$ we show that the new heuristic is an improvement over previous
heuristics for linear layouts.
