A linear algorithm for bipartition of biconnected graphs

Suzuki, Hitoshi; Takahashi, Norikazu; Nishizeki, Takao

doi:10.1016/0020-0190(90)90189-5

Cited by 46 publications

(22 citation statements)

References 2 publications

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“…However, neither of the proofs is constructive, and there are no known polynomial-time algorithms to find such a partition for k>3. For k=2, a linear time algorithm is provided in [17] and for k=3 an O(|V | 2 ) algorithm is provided in [19]. 1 The complexity of the problem with the size objective and related optimization problems have been studied in [3,5,6] and there are various NP-hardness and inapproximability results.…”

Section: V2|mentioning

confidence: 99%

Doubly Balanced Connected Graph Partitioning

Soltan

Yannakakis

Zussman

2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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We introduce and study the Doubly Balanced Connected graph Partitioning (DBCP) problem: Let G=(V, E) be a connected graph with a weight (supply/demand) function p:V →{−1, +1} satisfying|V1| }≤c s , for some constants c p and c s . When G is 2-connected, we show that a solution with c p =1 and c s =3 always exists and can be found in polynomial time. Moreover, when G is 3-connected, we show that there is always a 'perfect' solution (a partition with p(V 1 )=p(V 2 )=0 and |V 1 |=|V 2 |, if |V |≡0(mod 4)), and it can be found in polynomial time. Our techniques can be extended, with similar results, to the case in which the weights are arbitrary (not necessarily ±1), and to the case that p(V ) =0 and the excess supply/demand should be split evenly. They also apply to the problem of partitioning a graph with two types of nodes into two large connected subgraphs that preserve approximately the proportion of the two types.

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Section: V2|mentioning

confidence: 99%

Doubly Balanced Connected Graph Partitioning

Soltan

Yannakakis

Zussman

2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…In fact, with additional restrictions, i.e., that one may fix any representative for each subset of an expected vertex partition, they showed that the two properties are equivalent, see [6] or [8] for details. For the small values of k also the polynomial-time algorithms have been given, in particular, for k = 2, k = 3 [9,13], and for the case k = 4 restricted to the planar graphs [10].…”

Section: Introductionmentioning

confidence: 99%

On minimal arbitrarily partitionable graphs

Baudon

Przybyło

Woniak

2012

Information Processing Letters

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“…(i) There is a linear-time algorithm to find a bipartition of a 6th International Conference on Electrical and Computer Engineering ICECE 2010, 18-20 December 2010, Dhaka, Bangladesh biconnected graph [11], [12]. (ii) There is an O(n 2 ) time algorithm to find a 3-partition of a triconnected graph [12].…”

Section: Introductionmentioning

confidence: 99%

A linear algorithm for resource four-partitioning four-connected planar graphs

Awal

Rahman

2010

International Conference on Electrical &Amp; Computer Engineering (ICECE 2010)

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Given a connected graph G = (V, E), a set Vr ⊆ V of r special vertices, four distinct base vertices u 1, u2, u3, u4 ∈ V and four natural numbers r 1, r2, r3, r4 such that 4 j=1 rj = r, we wish to find a partition V 1, V2, V3, V4 of V such that Vi contains u i and ri vertices from Vr, and Vi induces a connected subgraph of G for each i, 1 ≤ i ≤ 4. We call a vertex in V r a resource vertex and the problem above of partitioning vertices of G as the resource four-partitioning problem. In this paper, we give a linear algorithm for finding a resource four-partition of a fourconnected planar graph G with base vertices located on the same face of a planar embedding. Our algortihm is based on a 4-canonical decomposition and st-numbering of G.

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A linear algorithm for bipartition of biconnected graphs

Cited by 46 publications

References 2 publications

Doubly Balanced Connected Graph Partitioning

Doubly Balanced Connected Graph Partitioning

On minimal arbitrarily partitionable graphs

A linear algorithm for resource four-partitioning four-connected planar graphs

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