Given a collection of multisets $\{X_1,X_2,\dots ,X_k\}$ ($k\ge 2$) of positive integers, a multiset S is a common integer partition for them if S is an integer partition of every multiset $X_i,1\le i\le k$. The minimum common integer partition (k-MCIP) problem is defined as to find a CIP for $\{X_1,X_2,\dots ,X_k\}$ with the minimum cardinality. We present a $\frac{6}{5}$-approximation algorithm for the 2-MCIP problem, improving the previous best algorithm of performance ratio $\frac{5}{4}$ designed by Chen et al. in 2006. We then extend it to obtain an absolute 0.6k-approximation algorithm for k-MCIP when k is even (when k is odd, the approximation ratio is $0.6k+0.4$).

给定一个多集集合 $\{X_1,X_2,\dots ,X_{克}\}$ ($克\ge 2$正整数），一个多重小号是一个常见的整数分区为他们，如果小号是每个多集的整数分区$X_{\mathrm{一世}},1\le \mathrm{一世}\le 克$. 的最低限度的共同整数分区（ķ -MCIP）的问题被定义为找到一个CIP为$\{X_1,X_2,\dots ,X_{克}\}$具有最小基数。我们提出一个$\frac{6}{5}$- 2-MCIP问题的近似算法，提高了之前性能比最好的算法 $\frac{5}{4}$由 Chen 等人设计。于2006年，然后扩展它来获得绝对0.6 ķ近似算法为ķ -MCIP当ķ为偶数（当ķ为奇数，则近似比为$0.6克+0.4$）。