3 research outputs found
Neighbourhood Broadcasting in Hypercubes
International audienceIn the broadcasting problem, one node needs to broadcast a message to all other nodes in a network. If nodes can only communicate with one neighbor at a time, broadcasting takes at least rounds in a network of nodes. In the neighborhood broadcasting problem, the node that is broadcasting needs to inform only its neighbors. In a binary hypercube with nodes, each node has neighbors, so neighborhood broadcasting takes at least rounds. In this paper, we present asymptotically optimal neighborhood broadcast protocols for binary hypercubes
Properties and algorithms of the (n, k)-arrangement graphs
The (n, k)-arrangement interconnection topology was first introduced in 1992. The
(n, k )-arrangement graph is a class of generalized star graphs. Compared with the
well known n-star, the (n, k )-arrangement graph is more flexible in degree and diameter.
However, there are few algorithms designed for the (n, k)-arrangement graph
up to present. In this thesis, we will focus on finding graph theoretical properties
of the (n, k)- arrangement graph and developing parallel algorithms that run on this
network.
The topological properties of the arrangement graph are first studied. They include
the cyclic properties. We then study the problems of communication: broadcasting
and routing. Embedding problems are also studied later on. These are very
useful to develop efficient algorithms on this network.
We then study the (n, k )-arrangement network from the algorithmic point of view.
Specifically, we will investigate both fundamental and application algorithms such as
prefix sums computation, sorting, merging and basic geometry computation: finding
convex hull on the (n, k )-arrangement graph.
A literature review of the state-of-the-art in relation to the (n, k)-arrangement
network is also provided, as well as some open problems in this area
Properties and algorithms of the (n, k)-star graphs
The (n, k)-star interconnection network was proposed in 1995 as an attractive alternative
to the n-star topology in parallel computation. The (n, k )-star has significant
advantages over the n-star which itself was proposed as an attractive alternative to
the popular hypercube. The major advantage of the (n, k )-star network is its scalability,
which makes it more flexible than the n-star as an interconnection network. In
this thesis, we will focus on finding graph theoretical properties of the (n, k )-star as
well as developing parallel algorithms that run on this network.
The basic topological properties of the (n, k )-star are first studied. These are
useful since they can be used to develop efficient algorithms on this network. We then
study the (n, k )-star network from algorithmic point of view. Specifically, we will
investigate both fundamental and application algorithms for basic communication,
prefix computation, and sorting, etc.
A literature review of the state-of-the-art in relation to the (n, k )-star network as
well as some open problems in this area are also provided