Parameterized Compilation Lower Bounds for Restricted CNF-formulas

We show unconditional parameterized lower bounds in the area of knowledge compilation, more specifically on the size of circuits in decomposable negation normal form (DNNF) that encode CNF-formulas restricted by several graph width measures. In particular, we show that - there are CNF formulas of size $n$ and modular incidence treewidth $k$ whose smallest DNNF-encoding has size $n^{\Omega(k)}$, and - there are CNF formulas of size $n$ and incidence neighborhood diversity $k$ whose smallest DNNF-encoding has size $n^{\Omega(\sqrt{k})}$. These results complement recent upper bounds for compiling CNF into DNNF and strengthen---quantitatively and qualitatively---known conditional low\-er bounds for cliquewidth. Moreover, they show that, unlike for many graph problems, the parameters considered here behave significantly differently from treewidth

Linear MIM-Width of Trees

We provide an $O(n \log n)$ algorithm computing the linear maximum induced matching width of a tree and an optimal layout.Comment: 19 pages, 7 figures, full version of WG19 paper of same nam

Clique-width : harnessing the power of atoms.

Many NP-complete graph problems are polynomial-time solvable on graph classes of bounded clique-width. Several of these problems are polynomial-time solvable on a hereditary graph class G if they are so on the atoms (graphs with no clique cut-set) of G . Hence, we initiate a systematic study into boundedness of clique-width of atoms of hereditary graph classes. A graph G is H-free if H is not an induced subgraph of G, and it is (H1,H2) -free if it is both H1 -free and H2 -free. A class of H-free graphs has bounded clique-width if and only if its atoms have this property. This is no longer true for (H1,H2) -free graphs, as evidenced by one known example. We prove the existence of another such pair (H1,H2) and classify the boundedness of clique-width on (H1,H2) -free atoms for all but 18 cases

Environmental effects and individual body condition drive seasonal fecundity of rabbits: identifying acute and lagged processes

The reproduction of many species is determined by seasonally-driven resource supply. But it is difficult to quantify whether the fecundity is sensitive to short- or long-term exposure to environmental conditions such as rainfall that drive resource supply. Using 25 years of data on individual fecundity of European female rabbits, Oryctolagus cuniculus, from semiarid Australia, we investigate the role of individual body condition, rainfall and temperature as drivers of seasonal and long-term and population-level changes in fecundity (breeding probability, ovulation rate, embryo survival). We built distributed lag models in a hierarchical Bayesian framework to account for both immediate and time-lagged effects of climate and other environmental drivers, and possible shifts in reproduction over consecutive seasons. We show that rainfall during summer, when rabbits typically breed only rarely, increased breeding probability immediately and with time lags of up to 10 weeks. However, an earlier onset of the yearly breeding period did not result in more overall reproductive output. Better body condition was associated with an earlier onset of breeding and higher embryo survival. Breeding probability in the main breeding season declined with increased breeding activity in the preceding season and only individuals in good body condition were able to breed late in the season. Higher temperatures reduce breeding success across seasons. We conclude that a better understanding of seasonal dynamics and plasticity (and their interplay) in reproduction will provide crucial insights into how lagomorphs are likely to respond and potentially adapt to the influence of future climate and other environmental change.Konstans Wells, Robert B. O’Hara, Brian D. Cooke, Greg J. Mutze, Thomas A.A. Prowse, Damien A. Fordha

Revisiting Graph Width Measures for CNF-Encodings

International audienceWe consider bounded width CNF-formulas where the width is measured by popular graph width measures on graphs associated to CNF-formulas. Such restricted graph classes, in particular those of bounded treewidth, have been extensively studied for their uses in the design of algorithms for various computational problems on CNF-formulas. Here we consider the expressivity of these formulas in the model of clausal encodings with auxiliary variables. We first show that bounding the width for many of the measures from the literature leads to a dramatic loss of expressivity, restricting the formulas to such of low communication complexity. We then show that the width of optimal encodings with respect to different measures is strongly linked: there are two classes of width measures, one containing primal treewidth and the other incidence cliquewidth, such that in each class the width of optimal encodings only differs by constant factors. Moreover, between the two classes the width differs at most by a factor logarithmic in the number of variables. Both these results are in stark contrast to the setting without auxiliary variables where all width measures we consider here differ by more than constant factors and in many cases even by linear factors