  This paper is concerned with subsequences that consist of limited numbers of
segments. We call a subsequence {$f$-segmental} if it is composed of $f$
factors. More precisely, any string of the form $u_1 \dots u_f$ is an
$f$-segmental subsequence of a string $v_0u_1v_1 \dots u_fv_f$. Since factors
are $1$-segmental subsequences, this relativizes the notions of factors and
subsequences. This paper studies some basic problems concerning $f$-segmental
subsequences: namely, the longest common $(f_1,f_2)$-segmental subsequence
problem and the $f$-segmental subsequence matching problem. The former asks the
longest string that is an $f_i$-segmental subsequence of two input strings
$T_i$ with $i=1,2$. The latter asks whether an input string $P$ is an
$f$-segmental subsequence of the other input string $T$. We present
polynomial-time algorithms for those problems and show that the one for the
$f$-segmental subsequence matching problem is optimal modulo sub-polynomial
factors under the strong exponential-time hypothesis.
