Given an n-vertex digraph D and a non-negative integer k, the Minimum Directed Bisection problem asks if the vertices of D can be partitioned into two parts, say L and R, such that \({\vert {L} \vert }\) and \({\vert {R} \vert }\) differ by at most 1 and the number of arcs from R to L is at most k. This problem is known to be NP-hard even when \(k = 0\). We investigate the parameterized complexity of this problem on semicomplete digraphs. We show that Minimum Directed Bisection admits a sub-exponential time fixed-parameter tractable algorithm on semicomplete digraphs. We also show that Minimum Directed Bisection admits a polynomial kernel on semicomplete digraphs. To design the kernel, we use \((n,k,k^2)\)-splitters, which, to the best of our knowledge, have never been used before in the design of kernels. We also prove that Minimum Directed Bisection is NP-hard on semicomplete digraphs, but polynomial time solvable on tournaments.

给定一个n顶点有向图D和一个非负整数k，则M个最小D切向的B isection问题询问D的顶点是否可以分为两部分，例如L和R，使得\（{\ vert {L } \ vert} \）和\（{\ vert {R} \ vert} \）相差最多1，并且从R到L的弧数最多为k。即使\（k = 0 \），也知道此问题是NP -hard问题。我们研究半完全有向图上此问题的参数化复杂性。我们表明，最小的D直交B截面积在半完全有向图上接受了次指数时间固定参数易处理算法。我们还表明，最小限度的D切开的B截面积在半完全有向图上接受多项式核。为了设计内核，我们使用\（（n，k，k ^ 2）\）- splitters，据我们所知，它从未在内核设计中使用过。我们也证明了中号的最小值d irected乙isection是NP-在半完全有向图中比较难，但是在锦标赛中可以解决多项式时间。