English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We introduce the graph parameter boolean-width, related to the number ofdifferent unions of neighborhoods across a cut of a graph. Boolean-width issimilar to rank-width, which is related to the number of $GF[2]$-sums (1+1=0)of neighborhoods instead of the boolean-sums (1+1=1) used for boolean-width. Wegive algorithms for a large class of NP-hard vertex subset and vertexpartitioning problems that are FPT when parameterized by either boolean-width,rank-width or clique-width, with runtime single exponential in either parameterif given the pertinent optimal decomposition. To compare boolean-width versusrank-width or clique-width, we first show that for any graph, the square rootof its boolean-width is never more than its rank-width. Next, we exhibit aclass of graphs, the Hsu-grids, for which we can solve NP-hard problems inpolynomial time, if we use the right parameter. An $n \times \frac{n}{10}$Hsu-grid on ${1/10}n^2$ vertices has boolean-width $\Theta(\log n)$ andrank-width $\Theta(n)$. Moreover, any optimal rank-decomposition of such agraph will have boolean-width $\Theta(n)$, i.e. exponential in the optimalboolean-width. A main open problem is to approximate the boolean-width betterthan what is given by the algorithm for rank-width [Hlin\v{e}n\'y and Oum,2008]

Fast FPT algorithms for vertex subset and vertex partitioning problems using neighborhood unions