  The $k$-Steiner-2NCS problem is as follows: Given a constant $k$, and an
undirected connected graph $G = (V,E)$, non-negative costs $c$ on $E$, and a
partition $(T, V-T)$ of $V$ into a set of terminals, $T$, and a set of
non-terminals (or, Steiner nodes), where $|T|=k$, find a minimum-cost two-node
connected subgraph that contains the terminals.
  We present a randomized polynomial-time algorithm for the unweighted problem,
and a randomized PTAS for the weighted problem.
  We obtain similar results for the $k$-Steiner-2ECS problem, where the input
is the same, and the algorithmic goal is to find a minimum-cost two-edge
connected subgraph that contains the terminals.
  Our methods build on results by Bj\"orklund, Husfeldt, and Taslaman (ACM-SIAM
SODA 2012) that give a randomized polynomial-time algorithm for the unweighted
$k$-Steiner-cycle problem; this problem has the same inputs as the unweighted
$k$-Steiner-2NCS problem, and the algorithmic goal is to find a minimum-size
simple cycle $C$ that contains the terminals ($C$ may contain any number of
Steiner nodes).
