Model Checking Lower Bounds for Simple Graphs

A well-known result by Frick and Grohe shows that deciding FO logic on trees involves a parameter dependence that is a tower of exponentials. Though this lower bound is tight for Courcelle's theorem, it has been evaded by a series of recent meta-theorems for other graph classes. Here we provide some additional non-elementary lower bound results, which are in some senses stronger. Our goal is to explain common traits in these recent meta-theorems and identify barriers to further progress. More specifically, first, we show that on the class of threshold graphs, and therefore also on any union and complement-closed class, there is no model-checking algorithm with elementary parameter dependence even for FO logic. Second, we show that there is no model-checking algorithm with elementary parameter dependence for MSO logic even restricted to paths (or equivalently to unary strings), unless E=NE. As a corollary, we resolve an open problem on the complexity of MSO model-checking on graphs of bounded max-leaf number. Finally, we look at MSO on the class of colored trees of depth d. We show that, assuming the ETH, for every fixed d>=1 at least d+1 levels of exponentiation are necessary for this problem, thus showing that the (d+1)-fold exponential algorithm recently given by Gajarsk\`{y} and Hlin\u{e}n\`{y} is essentially optimal

New Inapproximability Bounds for TSP

In this paper, we study the approximability of the metric Traveling Salesman Problem (TSP) and prove new explicit inapproximability bounds for that problem. The best up to now known hardness of approximation bounds were 185/184 for the symmetric case (due to Lampis) and 117/116 for the asymmetric case (due to Papadimitriou and Vempala). We construct here two new bounded occurrence CSP reductions which improve these bounds to 123/122 and 75/74, respectively. The latter bound is the first improvement in more than a decade for the case of the asymmetric TSP. One of our main tools, which may be of independent interest, is a new construction of a bounded degree wheel amplifier used in the proof of our results

Defective Coloring on Classes of Perfect Graphs

In Defective Coloring we are given a graph $G$ and two integers $\chi_d$, $\Delta^*$ and are asked if we can $\chi_d$-color $G$ so that the maximum degree induced by any color class is at most $\Delta^*$. We show that this natural generalization of Coloring is much harder on several basic graph classes. In particular, we show that it is NP-hard on split graphs, even when one of the two parameters $\chi_d$, $\Delta^*$ is set to the smallest possible fixed value that does not trivialize the problem ($\chi_d = 2$ or $\Delta^* = 1$). Together with a simple treewidth-based DP algorithm this completely determines the complexity of the problem also on chordal graphs. We then consider the case of cographs and show that, somewhat surprisingly, Defective Coloring turns out to be one of the few natural problems which are NP-hard on this class. We complement this negative result by showing that Defective Coloring is in P for cographs if either $\chi_d$ or $\Delta^*$ is fixed; that it is in P for trivially perfect graphs; and that it admits a sub-exponential time algorithm for cographs when both $\chi_d$ and $\Delta^*$ are unbounded

Urban challenges: main debates for sustainability and climate change adaptation

Aquest article il·lustra les connexions entre els impactes del canvi climàtic i el desenvolupament socioeconòmic i, a partir d’aquestes consideracions s’analitzen les relacions que aquests impactes tenen per als assentaments urbans. A la segona part, s’analitzen els temes d’adaptació i, mentre d’una banda es fa èmfasi en la relació entre Canvi Ambiental Global (GEC) canvi climàtic i adaptació, de l’altra es destaca com a l’interior d’aquestes dinàmiques hi ha una agenda de la desigualtat i de la justícia social. Finalment, en la tercera i última part de l’article, s’analitzen les dimensions de l’espai urbà, de la provisió d’energia i de l’accés a l’aigua i al sanejament, per mostrar la seva característica de dobles agendes del canvi climàtic, és a dir, de temàtiques front a les quals la racionalitat tècnica i la mirada a la dimensió física del problema del canvi climàtic no aconsegueix capturar la complexitat. L’article es proposa com un “concept paper”, és a dir, un treball que té com a objectiu mostrar connexions analítiques encara poc desenvolupades a l’interior d’una àrea d’investigació en ràpida construcció, com és el cas de l’adaptació de les ciutats al canvi climàtic.Este artículo ilustra las conexiones entre impactos del cambio climático y desarrollo socioeconómico y, a partir de estas consideraciones se analizan las relaciones que estos impactos tienen para los asentamientos urbanos. En la segunda parte, se analizan los temas de adaptación y, mientras por un lado se hace énfasis en la relación entre Cambio Ambiental Global (GEC) cambio climático y adaptación, por el otro se destaca como al interior de estas dinámicas existe una agenda de la desigualdad y de la justicia social. Finalmente, en la tercera y última parte del artículo, se analizan las dimensiones del espacio urbano, de la provisión de energía y del acceso al agua y al saneamiento, para mostrar su característica de dobles agendas del cambio climático, es decir, de temáticas frente a las cuales la racionalidad técnica y la mirada a la dimensión física del problema del cambo climático no logra capturar la complejidad. El artículo se propone como un “concept paper”, o sea, un trabajo que tiene como objetivo mostrar conexiones analíticas todavía poco desarrolladas al interior de un área de investigación en rápida construcción, como es el caso de la adaptación de las ciudades al cambio climático.This article illustrates the connections between climate change impacts and socioeconomic development and, and from these considerations, the relationships that these impacts have on urban settlements are analyzed. In the second part, the issues of adaptation are discussed; in one hand, it emphasizes the relationship between Global Environmental Change (GEC) climate change and adaptation, while on the other stands out that there is an agenda of inequality and social justice within these dynamics. Finally, the third and final part of the article explores the dimensions of urban space, energy supply and access to water and sanitation, to show how climate change agendas are double featured, meaning how looking at the physical dimension with technical rationality fail to capture the complexity of subjects related to the problem of climate change. The article is proposed as a “concept paper”, which aims to show analytical connections still poorly developed within a research area of rapid construction, such as the cities adaptation to climate change.Peer Reviewe