This paper compares three classes of algorithms for finding
Hamiltonian circuits in graphs. Two of the classes are exhaustive
search procedures and this study finds them to have an exponential
dependence on the size of the graph. The third class of algorithms,
based on Warnsdorff's rule, is found to be...
In real networks, identifying dense regions is of great importance. For example, in a network that represents academic collaboration, authors within the densest component of the graph tend to be the most prolific. Dense subgraphs often identify communities in social networks. And dense subgraphs can be used to discover regulatory...
There are growing interests in designing polynomial-time approximation schemes (PTAS) for optimization problems in planar graphs. Many NP-hard problems are shown to admit PTAS in planar graphs in the last decade, including Steiner tree, Steiner forest, two- edge-connected subgraphs and so on. We follow this research line and study several...
Given k terminal pairs (s₁,t₁),(s₂,t₂),..., (s[subscript k],t[subscript k]) in an edge-weighted graph G, the k Shortest Vertex-Disjoint Paths problem is to find a collection P₁, P₂,..., P[subscript k] of vertex-disjoint paths with minimum total length, where P[subscript i] is an s[subscript i]-to-t[subscript i] path. As a special case of the...
Molecular connectivity is a topological descriptor of
a molecule. It has been used as an independent variable
to describe biological activities, physicochemical
parameters (melting points, boiling points, partition
coefficients) and chromatographic retention indices. There
are inherent problems in using molecular connectivity. A
zero connectivity term has two opposing meanings: 1)...
The ability to interpret graphical information is a prime concern in physics as
graphs are widely used to give quick summaries of data sets, for pattern recognition, and for analysis of information. While visual graphs have been developed so that their content can be readily and concisely discerned, there is...
The set of codewords for a standard error-correcting code can be viewed
as subset of the vertices of a hypercube. Two vertices are adjacent in a hypercube exactly when their Hamming distance is 1. A code is a perfect-error-correcting code if no two codewords are adjacent and every non-codeword is...
Many algorithms in parallel systems can be easily solved if we can generate a Hamiltonian cycle on the underly network. Finding Hamiltonian cycle is a well known NP-complete problem. For specific instances of regular graphs, such as Torus and Gaussian network, one can easily find Hamiltonian cycles. In this thesis,...
The performance of transit networks must be measured on a regular basis to understand how well these complex systems fulfill their intended purpose and to identify potential opportunities for improvement. Measuring transit network performance is only achievable by defining a specific set of transit network performance indicators (TNPIs). Different schemes...