arXiv subjects

Irène Durand

Publications and source records attributed to Irène Durand.

3 recordsLinked to original sources

arXiv2021

A unified algorithm for colouring graphs of bounded clique-width

Clique-width is one of the graph complexity measures leading to polynomial special-case algorithms for generally NP-complete problems, e.g. graph colourability. The best two currently known algorithms for verifying c-colourability of graphs represented as clique-width terms are optimised towards two different extreme cases, a constant number of colours and a very large number of colours. We present a way to unify these approaches in a single relatively simple algorithm that achieves the state of the art complexity in both cases. The unified algorithm also provides a speed-up for a large number of colours.

cs.CC↗

arXiv2015

Computations by fly-automata beyond monadic second-order logic

We present logically based methods for constructing XP and FPT graph algorithms, parametrized by tree-width or clique-width. We will use fly-automata introduced in a previous article. They make possible to check properties that are not monadic second-order expressible because their states may include counters, so that their sets of states may be infinite. We equip these automata with output functions, so that they can compute values associated with terms or graphs. Rather than new algorithmic results we present tools for constructing easily certain dynamic programming algorithms by combining predefined automata for basic functions and properties.

cs.LO↗

arXiv2011

On the Complexity of Deciding Call-by-Need

In a recent paper we introduced a new framework for the study of call by need computations to normal form and root-stable form in term rewriting. Using elementary tree automata techniques and ground tree transducers we obtained simple decidability proofs for classes of rewrite systems that are much larger than earlier classes defined using the complicated sequentiality concept. In this paper we show that we can do without ground tree transducers in order to arrive at decidability proofs that are phrased in direct tree automata constructions. This allows us to derive better complexity bounds.

cs.LO↗