12 research outputs found
An algebraic view of the relation between largest common subtrees and smallest common supertrees
Abstract. The relationship between two important problems in tree pattern matching, the largest common subtree and the smallest common supertree problems, is established by means of simple constructions, which allow one to obtain a largest common subtree of two trees from a smallest common supertree of them, and vice versa. These constructions are the same for isomorphic, homeomorphic, topological, and minor embeddings, they take only time linear in the size of the trees, and they turn out to have a clear algebraic meaning.
New Algorithms andMethodology for Analysing Distances
Distances arise in a wide variety of di�erent contexts, one of which is partitional clustering,
that is, the problem of �nding groups of similar objects within a set of objects.¿ese
groups are seemingly very easy to �nd for humans, but very di�cult to �nd for machines
as there are two major di�culties to be overcome: the �rst de�ning an objective criterion
for the vague notion of “groups of similar objects”, and the second is the computational
complexity of �nding such groups given a criterion. In the �rst part of this thesis, we focus
on the �rst di�culty and show that even seemingly similar optimisation criteria used
for partitional clustering can produce vastly di�erent results. In the process of showing
this we develop a new metric for comparing clustering solutions called the assignment
metric. We then prove some new NP-completeness results for problems using two related
“sum-of-squares” clustering criteria.
Closely related to partitional clustering is the problem of hierarchical clustering. We
extend and formalise this problem to the problem of constructing rooted edge-weighted
X-trees, that is trees with a leafset X. It is well known that an X-tree can be uniquely
reconstructed from a distance on X if the distance is an ultrametric. But in practice the
complete distance on X may not always be available. In the second part of this thesis we
look at some of the circumstances under which a tree can be uniquely reconstructed from
incomplete distance information. We use a concept called a lasso and give some theoretical
properties of a special type of lasso. We then develop an algorithm which can construct
a tree together with a lasso from partial distance information and show how this can be
applied to various incomplete datasets
LIPIcs, Volume 244, ESA 2022, Complete Volume
LIPIcs, Volume 244, ESA 2022, Complete Volum
Global Constraint Catalog, 2nd Edition
This report presents a catalogue of global constraints where
each constraint is explicitly described in terms of graph properties and/or automata and/or first order logical formulae with arithmetic. When available, it also presents some typical usage as well as some pointers to existing
filtering algorithms