Graphs, and how to exploit their geometric representation. We will also see how to develop algorithms for several problems on strip The thesis takes significant steps towards characterizing, recognizing, and laying out This thesis studies algorithmic and structural aspects of varying the value τ Intersection graphs of unit-diameter disks whose centres are constrained to lie in a strip of More specifically, τ-strip graphs "interpolate" between unit disk graphs and indifference graphs they are the In which the second spatial dimension is gradually, introduced. To study these issues, this thesis identifies a range of subclasses of unit disk graphs Situation, and how can algorithms be designed to deal with it? Natural two-dimensional generalization of indifference graphs. NP-complete for the intersection graphs of unit disks in the plane (unit disk graphs), a Graphs do have efficient solutions on indifference graphs. Indifference graphs arise in a one-dimensional geometric context they are the intersection Problems remain NP-complete on geometric graphs. Solutions when restricted to such geometric graphs. It is reasonable to expect that natural graph problems have more efficient Physically routing traces on a printed circuit board (graph drawing), and modelling Such problems include assigning channels to radio transmitters (graph colouring), Computational problems on graphs often arise in two- or three-dimensional geometricĬontexts.
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