697 research outputs found
On the performance of routing algorithms in wormhole-switched multicomputer networks
This paper presents a comparative performance study of adaptive and deterministic routing algorithms in wormhole-switched hypercubes and investigates the performance vicissitudes of these routing schemes under a variety of network operating conditions. Despite the previously reported results, our results show that the adaptive routing does not consistently outperform the deterministic routing even for high dimensional networks. In fact, it appears that the superiority of adaptive routing is highly dependent to the broadcast traffic rate generated at each node and it begins to deteriorate by growing the broadcast rate of generated message
A class of hierarchical graphs as topologies for interconnection networks
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 particular, we study: the construction of shortest paths between arbitrary vertices in HCC(k,n); the connectivity of HCC(k,n); and one-to-all broadcasts in parallel machines whose underlying topology is HCC(k,n) (with both one-port and multi-port store-and-forward models of communication). Moreover, (some of) our proofs are applicable not just to hierarchical crossed cubes but to hierarchical interconnection networks formed by replacing crossed cubes with other families of interconnection networks. As such, we provide a generic construction with accompanying generic results relating to some topological and algorithmic properties of a wide range of hierarchical interconnection networks
Treewidth and related graph parameters
For modeling some practical problems, graphs play very important roles.
Since many modeled problems can be NP-hard in general, some restrictions
for inputs are required. Bounding a graph parameter of the inputs is one of
the successful approaches. We study this approach in this thesis. More precisely,
we study two graph parameters, spanning tree congestion and security
number, that are related to treewidth.
Let G be a connected graph and T be a spanning tree of G. For e ∈ E(T),
the congestion of e is the number of edges in G connecting two components
of T − e. The edge congestion of G in T is the maximum congestion over all
edges in T. The spanning tree congestion of G is the minimum congestion
of G in its spanning trees. In this thesis, we show the spanning tree congestion
for the complete k-partite graphs, the two-dimensional tori, and the twodimensional
Hamming graphs. We also address lower bounds of spanning
tree congestion for the multi-dimensional hypercubes, the multi-dimensional
grids, and the multi-dimensional Hamming graphs.
The security number of a graph is the cardinality of a smallest vertex subset
of the graph such that any “attack” on the subset is “defendable.” In this thesis,
we determine the security number of two-dimensional cylinders and tori.
This result settles a conjecture of Brigham, Dutton and Hedetniemi [Discrete
Appl. Math. 155 (2007) 1708–1714]. We also show that every outerplanar
graph has security number at most three. Additionally, we present lower and
upper bounds for some classes of graphs.学位記番号:工博甲39
Multi-Embedding of Metric Spaces
Metric embedding has become a common technique in the design of algorithms.
Its applicability is often dependent on how high the embedding's distortion is.
For example, embedding finite metric space into trees may require linear
distortion as a function of its size. Using probabilistic metric embeddings,
the bound on the distortion reduces to logarithmic in the size.
We make a step in the direction of bypassing the lower bound on the
distortion in terms of the size of the metric. We define "multi-embeddings" of
metric spaces in which a point is mapped onto a set of points, while keeping
the target metric of polynomial size and preserving the distortion of paths.
The distortion obtained with such multi-embeddings into ultrametrics is at most
O(log Delta loglog Delta) where Delta is the aspect ratio of the metric. In
particular, for expander graphs, we are able to obtain constant distortion
embeddings into trees in contrast with the Omega(log n) lower bound for all
previous notions of embeddings.
We demonstrate the algorithmic application of the new embeddings for two
optimization problems: group Steiner tree and metrical task systems
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