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On the Complexity of Universal Leader Election (2015)
Journal Article
Kutten, S., Pandurangan, G., Peleg, D., Robinson, P., & Trehan, A. (2015). On the Complexity of Universal Leader Election. Journal of the ACM, 62(1), 7:1-7:27

Graph editing to a fixed target (2014)
Journal Article
Golovach, P., Paulusma, D., & Stewart, I. (2017). Graph editing to a fixed target. Discrete Applied Mathematics, 216(Part 1), 181-190. https://doi.org/10.1016/j.dam.2014.07.008

For a fixed graph H, the H-Minor Edit problem takes as input a graph G and an integer k and asks whether G can be modified into H by a total of at most k edge contractions, edge deletions and vertex deletions. Replacing edge contractions by vertex di... Read More about Graph editing to a fixed target.

Multiswapped networks and their topological and algorithmic properties (2013)
Journal Article
Stewart, I. (2013). Multiswapped networks and their topological and algorithmic properties. Journal of Computer and System Sciences, 79(8), 1269-1286. https://doi.org/10.1016/j.jcss.2013.06.002

We generalise the biswapped network Bsw(G)Bsw(G) to obtain a multiswapped network Msw(H;G)Msw(H;G), built around two graphs G and H. We show that the network Msw(H;G)Msw(H;G) lends itself to optoelectronic implementation and examine its topological a... Read More about Multiswapped networks and their topological and algorithmic properties.

Interconnection networks of degree three obtained by pruning two-dimensional tori (2013)
Journal Article
Stewart, I. (2014). Interconnection networks of degree three obtained by pruning two-dimensional tori. IEEE Transactions on Computers, 63(10), 2473-9340. https://doi.org/10.1109/tc.2013.139

We study an interconnection network that we call 3Torus(m,n) obtained by pruning the 4m x 4n torus (of links) so that the resulting network is regular of degree 3. We show that 3Torus(m,n) retains many of the useful properties of tori (although, of c... Read More about Interconnection networks of degree three obtained by pruning two-dimensional tori.

On the computational complexity of routing in faulty k-ary n-cubes and hypercubes. (2012)
Journal Article
Stewart, I. (2012). On the computational complexity of routing in faulty k-ary n-cubes and hypercubes. Parallel Processing Letters, 22(1), Article 1250003. https://doi.org/10.1142/s012962641250003x

We equate a routing algorithm in a (faulty) interconnection network whose underlying graph is a k-ary n-cube or a hypercube, that attempts to route a packet from a fixed source node to a fixed destination node, with the sub-digraph of (healthy) links... Read More about On the computational complexity of routing in faulty k-ary n-cubes and hypercubes..

Bipancyclicity in k-ary n-cubes with faulty edges under a conditional fault assumption (2011)
Journal Article
Xiang, Y., & Stewart, I. (2011). Bipancyclicity in k-ary n-cubes with faulty edges under a conditional fault assumption. IEEE Transactions on Parallel and Distributed Systems, 22(9), 1506-1513. https://doi.org/10.1109/tpds.2011.22

We prove that a k-ary 2-cube Q^k_2 with 3 faulty edges but where every vertex is incident with at least 2 healthy edges is bipancyclic, if k \geq 3, and k-pancyclic, if k \geq 5 is odd (these results are optimal). We go on to show that when k \geq 4... Read More about Bipancyclicity in k-ary n-cubes with faulty edges under a conditional fault assumption.

A multipath analysis of biswapped networks (2011)
Journal Article
Xiang, Y., & Stewart, I. (2011). A multipath analysis of biswapped networks. The Computer Journal, 54(6), 920-930. https://doi.org/10.1093/comjnl/bxq083

Biswapped networks of the form $Bsw(G)$ have recently been proposed as interconnection networks to be implemented as optical transpose interconnection systems. We provide a systematic construction of $\kappa+1$ vertex-disjoint paths joining any two d... Read More about A multipath analysis of biswapped networks.

A class of hierarchical graphs as topologies for interconnection networks (2010)
Journal Article
Lai, P., Hsu, H., Tsai, C., & Stewart, I. (2010). A class of hierarchical graphs as topologies for interconnection networks. Theoretical Computer Science, 411(31-33), 2912-2924. https://doi.org/10.1016/j.tcs.2010.04.022

We study some topological and algorithmic properties of a recently defined hierarchical interconnection network, the hierarchical crossed cube HCC(k,n), which draws upon constructions used within the well-known hypercube and also the crossed cube. In... Read More about A class of hierarchical graphs as topologies for interconnection networks.

One-to-many node-disjoint paths in (n,k)-star graphs (2010)
Journal Article
Stewart, I., & Xiang, Y. (2010). One-to-many node-disjoint paths in (n,k)-star graphs. Discrete Applied Mathematics, 158(1), 62-70. https://doi.org/10.1016/j.dam.2009.08.013

We present an algorithm which given a source node and a set of n−1 target nodes in the (n,k)-star graph Sn,k, where all nodes are distinct, builds a collection of n−1 node-disjoint paths, one from each target node to the source. The collection of pat... Read More about One-to-many node-disjoint paths in (n,k)-star graphs.