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A Polynomial-Time Algorithm for Planar Multicuts with Few Source-Sink Pairs

機(jī)譯：少數(shù)源匯對(duì)的平面多型多項(xiàng)式算法

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摘要

Given an edge-weighted undirected graph and a list of k source-sink pairs ofvertices, the well-known minimum multicut problem consists in selecting aminimum-weight set of edges whose removal leaves no path between every sourceand its corresponding sink. We give the first polynomial-time algorithm tosolve this problem in planar graphs, when k is fixed. Previously, this problemwas known to remain NP-hard in general graphs with fixed k, and in trees witharbitrary k; the most noticeable tractable case known so far was in planargraphs with fixed k and sources and sinks lying on the outer face.

機(jī)譯：給定一個(gè)邊沿加權(quán)的無(wú)向圖和k個(gè)源-匯頂點(diǎn)對(duì)的列表，眾所周知的最小多切問(wèn)題在于選擇一組最小權(quán)重的邊，將其刪除不會(huì)在每個(gè)源及其對(duì)應(yīng)匯之間留下任何路徑。當(dāng)k固定時(shí)，我們給出了第一個(gè)多項(xiàng)式時(shí)間算法來(lái)解決平面圖中的這個(gè)問(wèn)題。以前，已知此問(wèn)題在固定k的一般圖中和任意k的樹中仍然是NP-hard的。迄今為止，最明顯的易處理案例是在平面圖中固定k且源和匯位于外表面的情況。

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作者
Cédric Bentz;
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年度 2012
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原文格式 PDF
正文語(yǔ)種 {"code":"en","name":"english","id":9}
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專利

1. An FPT Algorithm for Planar Multicuts with Sources and Sinks on the Outer Face [J] . Bentz Cedric Algorithmica . 2019,第1期

機(jī)譯：外表面帶有源和匯的平面多切口的FPT算法
2. A simple algorithm for multicuts in planar graphs with outer terminals [J] . Bentz C Discrete Applied Mathematics . 2009,第8期

機(jī)譯：具有外部端子的平面圖中多割的簡(jiǎn)單算法
3. A Sublinear-space and Polynomial-time Separator Algorithm for Planar Graphs [J] . Ryo Ashida, Tatsuya Imai, Kotaro Nakagawa, Electronic Colloquium on Computational Complexity . 2019,第3期

機(jī)譯：平面圖的次線性空間和多項(xiàng)式時(shí)間分離器算法
4. A Polynomial-Time Algorithm for Planar Multicuts with Few Source-Sink Pairs [C] . Cedric Bentz International Symposium on Parameterized and Exact Computation . 2012

機(jī)譯：少數(shù)源匯對(duì)的平面多型多項(xiàng)式算法
5. Primality Testing is Polynomial-time: A Mechanised Verification of the AKS Algorithm [D] . Chan, Hing Lun. 2019

機(jī)譯：原始測(cè)試是多項(xiàng)式 - 時(shí)間：AKS算法的機(jī)械化驗(yàn)證
6. Polynomial-Time Algorithms for Building a Consensus MUL-Tree [O] . Yun Cui, Jesper Jansson, Wing-Kin Sung -1

機(jī)譯：建立共識(shí)MUL樹的多項(xiàng)式時(shí)間算法
7. A polynomial-time algorithm for planar multicuts with few source-sink pairs [O] . Bentz, Cédric 2012

機(jī)譯：具有少量源 - 匯的平面多核的多項(xiàng)式時(shí)間算法 ??對(duì)

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A Polynomial-Time Algorithm for Planar Multicuts with Few Source-Sink Pairs

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