  Given an edge-weighted (metric/general) complete graph with $n$ vertices, the
maximum weight (metric/general) $k$-cycle/path packing problem is to find a set
of $\frac{n}{k}$ vertex-disjoint $k$-cycles/paths such that the total weight is
maximized. In this paper, we consider approximation algorithms. For metric
$k$-cycle packing, we improve the previous approximation ratio from $3/5$ to
$7/10$ for $k=5$, and from $7/8\cdot(1-1/k)^2$ for $k>5$ to
$(7/8-0.125/k)(1-1/k)$ for constant odd $k>5$ and to $7/8\cdot
(1-1/k+\frac{1}{k(k-1)})$ for even $k>5$. For metric $k$-path packing, we
improve the approximation ratio from $7/8\cdot (1-1/k)$ to
$\frac{27k^2-48k+16}{32k^2-36k-24}$ for even $10\geq k\geq 6$. For the case of
$k=4$, we improve the approximation ratio from $3/4$ to $5/6$ for metric
4-cycle packing, from $2/3$ to $3/4$ for general 4-cycle packing, and from
$3/4$ to $14/17$ for metric 4-path packing.
