We study the expected value of the lengthLnof the minimum spanning tree of the complete graphKnwh... more We study the expected value of the lengthLnof the minimum spanning tree of the complete graphKnwhen each edgeeis given an independent uniform [0, 1] edge weight. We sharpen the result of Frieze [6] that limn→∞$\mathbb{E}$(Ln) = ζ(3) and show that$$ \mathbb{E}(L_n)=\zeta(3)+\frac{c_1}{n}+\frac{c_2+o(1)}{n^{4/3}}, $$wherec1,c2are explicitly defined constants.
Let the edges of a graph $G$ be coloured so that no colour is used more than $k$ times. We refer ... more Let the edges of a graph $G$ be coloured so that no colour is used more than $k$ times. We refer to this as a $k$-bounded colouring. We say that a subset of the edges of $G$ is multicoloured if each edge is of a different colour. We say that the colouring is $\cal H$-good, if a multicoloured Hamilton cycle exists i.e., one with a multicoloured edge-set. Let ${\cal AR}_k$ = $\{G :$ every $k$-bounded colouring of $G$ is $\cal H$-good$\}$. We establish the threshold for the random graph $G_{n,m}$ to be in ${\cal AR}_k$.
This paper studies broadcasting and gossiping algorithms in random and general AdHoc networks. Ou... more This paper studies broadcasting and gossiping algorithms in random and general AdHoc networks. Our goal is not only to minimise the broadcasting and gossiping time, but also to minimise the energy consumption, which is measured in terms of the total number of messages (or transmissions) sent. We assume that the nodes of the network do not know the network, and
We study the expected value of the lengthLnof the minimum spanning tree of the complete graphKnwh... more We study the expected value of the lengthLnof the minimum spanning tree of the complete graphKnwhen each edgeeis given an independent uniform [0, 1] edge weight. We sharpen the result of Frieze [6] that limn→∞$\mathbb{E}$(Ln) = ζ(3) and show that$$ \mathbb{E}(L_n)=\zeta(3)+\frac{c_1}{n}+\frac{c_2+o(1)}{n^{4/3}}, $$wherec1,c2are explicitly defined constants.
Let the edges of a graph $G$ be coloured so that no colour is used more than $k$ times. We refer ... more Let the edges of a graph $G$ be coloured so that no colour is used more than $k$ times. We refer to this as a $k$-bounded colouring. We say that a subset of the edges of $G$ is multicoloured if each edge is of a different colour. We say that the colouring is $\cal H$-good, if a multicoloured Hamilton cycle exists i.e., one with a multicoloured edge-set. Let ${\cal AR}_k$ = $\{G :$ every $k$-bounded colouring of $G$ is $\cal H$-good$\}$. We establish the threshold for the random graph $G_{n,m}$ to be in ${\cal AR}_k$.
This paper studies broadcasting and gossiping algorithms in random and general AdHoc networks. Ou... more This paper studies broadcasting and gossiping algorithms in random and general AdHoc networks. Our goal is not only to minimise the broadcasting and gossiping time, but also to minimise the energy consumption, which is measured in terms of the total number of messages (or transmissions) sent. We assume that the nodes of the network do not know the network, and
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Papers by Colin Cooper