# Disjoint Paths Routing in Pancake Graphs

@article{Kaneko2006DisjointPR, title={Disjoint Paths Routing in Pancake Graphs}, author={Keiichi Kaneko and Shietung Peng}, journal={2006 Seventh International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT'06)}, year={2006}, pages={254-259} }

In this paper, we propose efficient algorithms that find disjoint paths for node-to-node and node-to-set routing in pancake graphs. For an n-pancake graph, the algorithms can find n - 1 disjoint paths of small maximum length with optimal time complexity. That is, the n - 1 paths can be constructed in O(n2) time and the maximum length is bounded by 5n/3 + 6

## 15 Citations

Set-to-Set Disjoint Paths Routing in Dual-Cubes

- Computer Science2008 Ninth International Conference on Parallel and Distributed Computing, Applications and Technologies
- 2008

An efficient algorithm that finds disjoint paths for set-to-set routing in a dual-cube with about half of links per node compared with the hypercube containing equal number of nodes is proposed.

Fault-Tolerant Routing in (n, k) - Star Graphs

- Computer Science2014 15th International Conference on Parallel and Distributed Computing, Applications and Technologies
- 2014

A fault-tolerant routing algorithm is proposed that establishes a fault-free path between any pair of non-faulty nodes in an Sn, k with faulty nodes by using limited global information called safety vectors.

The Set-to-Set Disjoint-Path Problem in Perfect Hierarchical Hypercubes

- Computer ScienceComput. J.
- 2012

An algorithm solving the set-to-set disjoint-path routing problem in perfect HHCs is described, which can find m+1 node-disjoint paths between the nodes of S and the node of D of lengths at most in O(m2 22m) time complexity.

A routing algorithm of pairwise disjoint paths in a burnt pancake graph

- Computer ScienceSoICT '11
- 2011

An algorithm that solves the k-pariwise disjoint path problem in an n-burnt pancake graph in polynomial-order time of <i>n</i> is proposed and a proof of its correctness is given.

A Set-to-Set Disjoint Paths Routing Algorithm in Tori

- Computer ScienceInt. J. Netw. Comput.
- 2017

It is proved that the paths selected by the proposed algorithm have lengths at most 2( k +1) n and can be obtained with a time complexity of O ( kn 3 n 3 log n ).

The constructive algorithm of vertex-disjoint paths in the generalized hypercube under restricted connectivity

- Mathematics, Computer Science
- 2019

An algorithm is designed to construct at least k^1(G) disjoint paths based on any two distinct vertices in G(m, m_r-1,...,m_1) under the 1-restricted connectivity.

Constructing Independent Spanning Trees on Pancake Networks

- Computer ScienceIEEE Access
- 2020

This paper proposes algorithms for constructing ISTs on pancake graph and presents proofs about the construction of ISTs in different dimensions to verify that the correctness of these algorithms are correct.

Mutually Independent Hamiltonian Cycle of Burnt Pancake Graphs

- MathematicsIEICE Trans. Fundam. Electron. Commun. Comput. Sci.
- 2011

This paper proved that IHC (B2)=1 and IHC(Bn)=n for n≥3 and that the mutually independent hamiltonicity of a graph G is the maximum integer k such that for any vertex u of G there are k mutually independent Hamiltonian cycles of G starting at u.

Set-to-Set Disjoint Paths in Tori

- Computer Science2016 Fourth International Symposium on Computing and Networking (CANDAR)
- 2016

This paper proposes an algorithm that constructs 2n mutually node-disjoint paths from a set S of 2n source nodes to a set D of2n destination nodes in an n-dimensional k-ary torus Tn,k (n¡Ã 1, k ¡Ã 3).

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