arXiv subjects

Maurice Chandoo

Publications and source records attributed to Maurice Chandoo.

6 recordsLinked to original sources

arXiv2020

A Systematic Approach to Programming

We show how to systematically implement an algorithm in any imperative or functional programming language. The method is based on the premise that it is easy to write down how an algorithm proceeds on a concrete input. This information---which we call execution trace---is used as a starting point to derive the desired program. In contrast to test-driven development the program is directly constructed from the test cases instead of written separately. The program's operations, control flow and predicates guiding the control flow are worked out separately, which saves the programmer from having to think about them simultaneously. We demonstrate the method for two examples and discuss its utility. Additionally, we provide a formal framework to compare it with other approaches.

cs.SE↗

arXiv2019

Fundamentals of Parameterized Complexity Revisited

Flum and Grohe define a parameter (parameterization) as a function $κ$ which maps words over a given alphabet to natural numbers. They require such functions to be polynomial-time computable. We show how this technical restriction can be lifted without breaking the theory. More specifically, instead of $κ$ we consider the set of languages that it bounds as parameterization and define the basic notions of parameterized complexity in terms of promise problems, which completely replace slices. One advantage of this formalization is that it becomes possible to interpret any complexity-theoretic concept which can be considered on a restricted set of inputs as a parameterized concept. Moreover, this formalization provides a unified way to apply the parameterization paradigm to other kinds of complexity such as enumeration or approximation by simply defining promise problems.

cs.CC↗

arXiv2018

A Complexity Theory for Labeling Schemes

In a labeling scheme the vertices of a given graph from a particular class are assigned short labels such that adjacency can be algorithmically determined from these labels. A representation of a graph from that class is given by the set of its vertex labels. Due to the shortness constraint on the labels such schemes provide space-efficient representations for various graph classes, such as planar or interval graphs. We consider what graph classes cannot be represented by labeling schemes when the algorithm which determines adjacency is subjected to computational constraints.

cs.CC↗

arXiv2017

Canonical Representations for Circular-Arc Graphs Using Flip Sets

We show that computing canonical representations for circular-arc (CA) graphs reduces to computing certain subsets of vertices called flip sets. For a broad class of CA graphs, which we call uniform, it suffices to compute a CA representation to find such flip sets. As a consequence canonical representations for uniform CA graphs can be obtained in polynomial-time. We then investigate what kind of CA graphs pose a challenge to this approach. This leads us to introduce the notion of restricted CA matrices and show that the canonical representation problem for CA graphs is logspace-reducible to that of restricted CA matrices. As a byproduct, we obtain the result that CA graphs without induced 4-cycles can be canonized in logspace.

cs.DS↗

arXiv2016

On the Implicit Graph Conjecture

The implicit graph conjecture states that every sufficiently small, hereditary graph class has a labeling scheme with a polynomial-time computable label decoder. We approach this conjecture by investigating classes of label decoders defined in terms of complexity classes such as P and EXP. For instance, GP denotes the class of graph classes that have a labeling scheme with a polynomial-time computable label decoder. Until now it was not even known whether GP is a strict subset of GR. We show that this is indeed the case and reveal a strict hierarchy akin to classical complexity. We also show that classes such as GP can be characterized in terms of graph parameters. This could mean that certain algorithmic problems are feasible on every graph class in GP. Lastly, we define a more restrictive class of label decoders using first-order logic that already contains many natural graph classes such as forests and interval graphs. We give an alternative characterization of this class in terms of directed acyclic graphs. By showing that some small, hereditary graph class cannot be expressed with such label decoders a weaker form of the implicit graph conjecture could be disproven.

cs.CC↗

arXiv2015

Deciding Circular-Arc Graph Isomorphism in Parameterized Logspace

We compute a canonical circular-arc representation for a given circular-arc (CA) graph which implies solving the isomorphism and recognition problem for this class. To accomplish this we split the class of CA graphs into uniform and non-uniform ones and employ a generalized version of the argument given by Köbler et al (2013) that has been used to show that the subclass of Helly CA graphs can be canonized in logspace. For uniform CA graphs our approach works in logspace and in addition to that Helly CA graphs are a strict subset of uniform CA graphs. Thus our result is a generalization of the canonization result for Helly CA graphs. In the non-uniform case a specific set of ambiguous vertices arises. By choosing the parameter to be the cardinality of this set the obstacle can be solved by brute force. This leads to an O(k + log n) space algorithm to compute a canonical representation for non-uniform and therefore all CA graphs.

cs.DS↗