Structure Theorem and Isomorphism Test for Graphs with Excluded Topological Subgraphs

We generalize the structure theorem of Robertson and Seymour for graphs excluding a fixed graph $H$ as a minor to graphs excluding $H$ as a topological subgraph. We prove that for a fixed $H$, every graph excluding $H$ as a topological subgraph has a tree decomposition where each part is either "almost embeddable" to a fixed surface or has bounded degree with the exception of a bounded number of vertices. Furthermore, we prove that such a decomposition is computable by an algorithm that is fixed-parameter tractable with parameter $|H|$. We present two algorithmic applications of our structure theorem. To illustrate the mechanics of a "typical" application of the structure theorem, we show that on graphs excluding $H$ as a topological subgraph, Partial Dominating Set (find $k$ vertices whose closed neighborhood has maximum size) can be solved in time $f(H,k)\cdot n^{O(1)}$ time. More significantly, we show that on graphs excluding $H$ as a topological subgraph, Graph Isomorphism can be solved in time $n^{f(H)}$. This result unifies and generalizes two previously known important polynomial-time solvable cases of Graph Isomorphism: bounded-degree graphs and $H$-minor free graphs. The proof of this result needs a generalization of our structure theorem to the context of invariant treelike decomposition

Deciding first-order properties of nowhere dense graphs

Nowhere dense graph classes, introduced by Nesetril and Ossona de Mendez, form a large variety of classes of "sparse graphs" including the class of planar graphs, actually all classes with excluded minors, and also bounded degree graphs and graph classes of bounded expansion. We show that deciding properties of graphs definable in first-order logic is fixed-parameter tractable on nowhere dense graph classes. At least for graph classes closed under taking subgraphs, this result is optimal: it was known before that for all classes C of graphs closed under taking subgraphs, if deciding first-order properties of graphs in C is fixed-parameter tractable, then C must be nowhere dense (under a reasonable complexity theoretic assumption). As a by-product, we give an algorithmic construction of sparse neighbourhood covers for nowhere dense graphs. This extends and improves previous constructions of neighbourhood covers for graph classes with excluded minors. At the same time, our construction is considerably simpler than those. Our proofs are based on a new game-theoretic characterisation of nowhere dense graphs that allows for a recursive version of locality-based algorithms on these classes. On the logical side, we prove a "rank-preserving" version of Gaifman's locality theorem.Comment: 30 page

Parameterized Directed kk-Chinese Postman Problem and kk Arc-Disjoint Cycles Problem on Euler Digraphs

In the Directed $k$-Chinese Postman Problem ($k$-DCPP), we are given a connected weighted digraph $G$ and asked to find $k$ non-empty closed directed walks covering all arcs of $G$ such that the total weight of the walks is minimum. Gutin, Muciaccia and Yeo (Theor. Comput. Sci. 513 (2013) 124--128) asked for the parameterized complexity of $k$-DCPP when $k$ is the parameter. We prove that the $k$-DCPP is fixed-parameter tractable. We also consider a related problem of finding $k$ arc-disjoint directed cycles in an Euler digraph, parameterized by $k$. Slivkins (ESA 2003) showed that this problem is W[1]-hard for general digraphs. Generalizing another result by Slivkins, we prove that the problem is fixed-parameter tractable for Euler digraphs. The corresponding problem on vertex-disjoint cycles in Euler digraphs remains W[1]-hard even for Euler digraphs

On First-Order Topological Queries

International audienceOne important class of spatial database queries is the class of topological queries, that is, queries invariant under homeomorphisms. We study topological queries expressible in the standard query language on spatial databases, rst-order logic with various amounts of arithmetic. Our main technical result is a combinato-rial characterization of the expressive power of topological rst-order logic on regular spatial databases

The Effects of Endogenous Firm Exit on Business Cycle Dynamics and Optimal Fiscal Policy

We explore the implications of endogenous firm entry and exit for business cycle dynamics and optimal fiscal policy. We first show that when the firm exit rate is endogenous, negative technology shocks lead to reductions in the number of firms. Technology shocks therefore have additional effects on household welfare relative to an economy with only endogenous entry. Second, endogenous firm exit creates a new channel for monetary policy when debt contracts are written in nominal terms, as monetary shocks affect the rate of firm defaults. Monetary shocks therefore have real effects also when prices and wages are flexible. Third, we show that endogenous firm exit creates a new role for fiscal policy to increase efficiency and welfare by subsidizing firms and decreasing the number of defaults. Finally, we demonstrate that endogenous firm exit implies that non-persistent shocks to technology and money supply have persistent effects on labor productivity. This has implications for the estimated persistence of technology shocks

Compact Labelings For Efficient First-Order Model-Checking

We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices. We prove that there exists such a labeling for checking a first-order formula with free set variables in the graphs of every class that is \emph{nicely locally cwd-decomposable}. This notion generalizes that of a \emph{nicely locally tree-decomposable} class. The graphs of such classes can be covered by graphs of bounded \emph{clique-width} with limited overlaps. We also consider such labelings for \emph{bounded} first-order formulas on graph classes of \emph{bounded expansion}. Some of these results are extended to counting queries

Logics for Unranked Trees: An Overview

Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for expressing navigational properties, and some make it easy to relate complex properties of trees to the existence of tree automata for those properties. Furthermore, logics differ significantly in their model-checking properties, their automata models, and their behavior on ordered and unordered trees. In this paper we present a survey of logics for unranked trees

Does Treewidth Help in Modal Satisfiability?

Many tractable algorithms for solving the Constraint Satisfaction Problem (CSP) have been developed using the notion of the treewidth of some graph derived from the input CSP instance. In particular, the incidence graph of the CSP instance is one such graph. We introduce the notion of an incidence graph for modal logic formulae in a certain normal form. We investigate the parameterized complexity of modal satisfiability with the modal depth of the formula and the treewidth of the incidence graph as parameters. For various combinations of Euclidean, reflexive, symmetric and transitive models, we show either that modal satisfiability is FPT, or that it is W[1]-hard. In particular, modal satisfiability in general models is FPT, while it is W[1]-hard in transitive models. As might be expected, modal satisfiability in transitive and Euclidean models is FPT.Comment: Full version of the paper appearing in MFCS 2010. Change from v1: improved section 5 to avoid exponential blow-up in formula siz

Visual Ontology Cleaning: Cognitive Principles and Applicability

In this paper we connect two research areas, the Qualitative Spatial Reasoning and visual reasoning on ontologies. We discuss the logical limitations of the mereotopological approach to the visual ontology cleaning, from the point of view of its formal support. The analysis is based on three different spatial interpretations wich are based in turn on three different spatial interpretations of the concepts of an ontology.Ministerio de Educación y Ciencia TIN2004-0388

54P Efficacy of first-line immunotherapy for non-small cell lung cancer with MET exon 14 skipping according to PD-L1 expression [Abstract]

Background METΔ14ex is the driver alteration for approximately 3% of non-small cell lung cancers (NSCLC) and associated with a higher PD-L1 expression, but unclear benefit from immunotherapy (IO). Methods Seventy-eight consecutive patients with metastatic NSCLC harboring METΔex14 who received first-line IO as monotherapy or chemoimmunotherapy (CHT+IO) in 10 German academic lung cancer centers were analyzed. Results The median age was 72 years (range 49-86), 34 patients (44%) were female, 47 (60%) were active or former smokers, and 23 (29%) presented with brain metastases. The Eastern Cooperative Group (ECOG) performance status was 0, 1, 2 and 3 in 27 (35%), 28 (36%), 18 (23%) and 4 (5%) cases, respectively. The most common histology was adenocarcinoma (n=61, 78%). IO was given to 43 (55%) patients as monotherapy, and to 35 (45%) combined with CHT. For patients with PD-L1 tumor proportion score (TPS) ≥50% (n=52, 67%), 1-49% (n=14, 18%) and <1% (n=12, 15%), disease control rates (DCR) were 56%, 57% and 100% (p=0.015), respectively. Other efficacy parameters including overall response rate (ORR), median progression-free survival (mPFS) and median overall survival (mOS) by PD-L1 tumor proportion score (TPS) and type of treatment are summarized in the table. Primary progressive disease/early death (before radiologic reassessment) under IO monotherapy, but not under CHT+IO, was significantly associated with never-smoker status (p=0.041). No significant correlations were found between smoking status and PD-L1 TPS (p=0.595). Conclusions Our exploratory analysis suggests an association between higher PD-L1 TPS and worse clinical outcomes under IO in patients with NSCLC harboring METΔ14ex. Although these results should be interpreted with caution, they contrast the favorable effect of PD-L1 expression for IO efficacy in other NSCLC and underline the need for alternative biomarkers for IO in this patient population