Reduction Techniques for Graph Isomorphism in the Context of Width Parameters

We study the parameterized complexity of the graph isomorphism problem when parameterized by width parameters related to tree decompositions. We apply the following technique to obtain fixed-parameter tractability for such parameters. We first compute an isomorphism invariant set of potential bags for a decomposition and then apply a restricted version of the Weisfeiler-Lehman algorithm to solve isomorphism. With this we show fixed-parameter tractability for several parameters and provide a unified explanation for various isomorphism results concerned with parameters related to tree decompositions. As a possibly first step towards intractability results for parameterized graph isomorphism we develop an fpt Turing-reduction from strong tree width to the a priori unrelated parameter maximum degree.Comment: 23 pages, 4 figure

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

Graphs Identified by Logics with Counting

We classify graphs and, more generally, finite relational structures that are identified by C2, that is, two-variable first-order logic with counting. Using this classification, we show that it can be decided in almost linear time whether a structure is identified by C2. Our classification implies that for every graph identified by this logic, all vertex-colored versions of it are also identified. A similar statement is true for finite relational structures. We provide constructions that solve the inversion problem for finite structures in linear time. This problem has previously been shown to be polynomial time solvable by Martin Otto. For graphs, we conclude that every C2-equivalence class contains a graph whose orbits are exactly the classes of the C2-partition of its vertex set and which has a single automorphism witnessing this fact. For general k, we show that such statements are not true by providing examples of graphs of size linear in k which are identified by C3 but for which the orbit partition is strictly finer than the Ck-partition. We also provide identified graphs which have vertex-colored versions that are not identified by Ck.Comment: 33 pages, 8 Figure

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

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

Tractability in Constraint Satisfaction Problems: A Survey

International audienceEven though the Constraint Satisfaction Problem (CSP) is NP-complete, many tractable classes of CSP instances have been identified. After discussing different forms and uses of tractability, we describe some landmark tractable classes and survey recent theoretical results. Although we concentrate on the classical CSP, we also cover its important extensions to infinite domains and optimisation, as well as #CSP and QCSP

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

Weisfeiler and Leman go Machine Learning

In recent years, algorithms and neural architectures based on the Weisfeiler-Leman algorithm, a well-known heuristic for the graph isomorphism problem, have emerged as a powerful tool for machine learning with graphs and relational data. Here, we give a comprehensive overview of the algorithm's use in a machine-learning setting, focusing on the supervised regime. We discuss the theoretical background, show how to use it for supervised graph and node representation learning, discuss recent extensions, and outline the algorithm's connection to (permutation-)equivariant neural architectures. Moreover, we give an overview of current applications and future directions to stimulate further research

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