43 research outputs found
SFCDecomp: Multicriteria Optimized Tool Path Planning in 3D Printing using Space-Filling Curve Based Domain Decomposition
We explore efficient optimization of toolpaths based on multiple criteria for
large instances of 3D printing problems. We first show that the minimum turn
cost 3D printing problem is NP-hard, even when the region is a simple polygon.
We develop SFCDecomp, a space filling curve based decomposition framework to
solve large instances of 3D printing problems efficiently by solving these
optimization subproblems independently. For the Buddha model, our framework
builds toolpaths over a total of 799,716 nodes across 169 layers, and for the
Bunny model it builds toolpaths over 812,733 nodes across 360 layers. Building
on SFCDecomp, we develop a multicriteria optimization approach for toolpath
planning. We demonstrate the utility of our framework by maximizing or
minimizing tool path edge overlap between adjacent layers, while jointly
minimizing turn costs. Strength testing of a tensile test specimen printed with
tool paths that maximize or minimize adjacent layer edge overlaps reveal
significant differences in tensile strength between the two classes of prints.Comment: Minor edits to incorporate reviewers' comments. Published in IJCG
Hypohamiltonian and almost hypohamiltonian graphs
This Dissertation is structured as follows. In Chapter 1, we give a short historical overview and define fundamental concepts. Chapter 2 contains a clear narrative of the progress made towards finding the smallest planar hypohamiltonian graph, with all of the necessary theoretical tools and techniques--especially Grinberg's Criterion. Consequences of this progress are distributed over all sections and form the leitmotif of this Dissertation. Chapter 2 also treats girth restrictions and hypohamiltonian graphs in the context of crossing numbers. Chapter 3 is a thorough discussion of the newly introduced almost hypohamiltonian graphs and their connection to hypohamiltonian graphs. Once more, the planar case plays an exceptional role. At the end of the chapter, we study almost hypotraceable graphs and Gallai's problem on longest paths. The latter leads to Chapter 4, wherein the connection between hypohamiltonicity and various problems related to longest paths and longest cycles are presented. Chapter 5 introduces and studies non-hamiltonian graphs in which every vertex-deleted subgraph is traceable, a class encompassing hypohamiltonian and hypotraceable graphs. We end with an outlook in Chapter 6, where we present a selection of open problems enriched with comments and partial results
Combinatorics, Probability and Computing
The main theme of this workshop was the use of probabilistic
methods in combinatorics and theoretical computer science. Although
these methods have been around for decades, they are being refined all
the time: they are getting more and more sophisticated and powerful.
Another theme was the study of random combinatorial structures,
either for their own sake, or to tackle extremal questions. The workshop
also emphasized connections between probabilistic combinatorics and
discrete probability
Hamiltonicity problems in random graphs
In this thesis, we present some of the main results proved by the author while fulfilling his PhD. While we present all the relevant results in the introduction of the thesis, we have chosen to focus on two of the main ones.
First, we show a very recent development about Hamiltonicity in random subgraphs of the hypercube, where we have resolved a long standing conjecture dating back to the 1980s.
Second, we present some original results about correlations between the appearance of edges in random regular hypergraphs, which have many applications in the study of subgraphs of random regular hypergraphs. In particular, these applications include subgraph counts and property testing