Bounding Generalized Coloring Numbers of Planar Graphs Using Coin Models

We study Koebe orderings of planar graphs: vertex orderings obtained bymodelling the graph as the intersection graph of pairwise internally-disjointdiscs in the plane, and ordering the vertices by non-increasing radii of theassociated discs. We prove that for every $d\in \mathbb{N}$, any such orderinghas $d$-admissibility bounded by $O(d/\ln d)$ and weak $d$-coloring numberbounded by $O(d^4 \ln d)$. This in particular shows that the $d$-admissibilityof planar graphs is bounded by $O(d/\ln d)$, which asymptotically matches aknown lower bound due to Dvo\v{r}\'ak and Siebertz.<br

Makespan Scheduling of Unit Jobs with Precedence Constraints in O(1.995n)O(1.995^n) time

In a classical scheduling problem, we are given a set of $n$ jobs of unitlength along with precedence constraints and the goal is to find a schedule ofthese jobs on $m$ identical machines that minimizes the makespan. This problemis well-known to be NP-hard for an unbounded number of machines. Using standard3-field notation, it is known as $P|\text{prec}, p_j=1|C_{\max}$. We present an algorithm for this problem that runs in $O(1.995^n)$ time.Before our work, even for $m=3$ machines the best known algorithms ran in$O^\ast(2^n)$ time. In contrast, our algorithm works when the number ofmachines $m$ is unbounded. A crucial ingredient of our approach is an algorithmwith a runtime that is only single-exponential in the vertex cover of thecomparability graph of the precedence constraint graph. This heavily relies oninsights from a classical result by Dolev and Warmuth (Journal of Algorithms1984) for precedence graphs without long chains.<br

A Gap-{ETH}-Tight Approximation Scheme for Euclidean {TSP}

We revisit the classic task of finding the shortest tour of $n$ points in $d$-dimensional Euclidean space, for any fixed constant $d \geq 2$. We determine the optimal dependence on $\varepsilon$ in the running time of an algorithm that computes a $(1+\varepsilon)$-approximate tour, under a plausible assumption. Specifically, we give an algorithm that runs in $2^{\mathcal{O}(1/\varepsilon^{d-1})} n\log n$ time. This improves the previously smallest dependence on $\varepsilon$ in the running time $(1/\varepsilon)^{\mathcal{O}(1/\varepsilon^{d-1})}n \log n$ of the algorithm by Rao and Smith (STOC 1998). We also show that a $2^{o(1/\varepsilon^{d-1})}\text{poly}(n)$ algorithm would violate the Gap-Exponential Time Hypothesis (Gap-ETH). Our new algorithm builds upon the celebrated quadtree-based methods initially proposed by Arora (J. ACM 1998), but it adds a simple new idea that we call \emph{sparsity-sensitive patching}. On a high level this lets the granularity with which we simplify the tour depend on how sparse it is locally. Our approach is (arguably) simpler than the one by Rao and Smith since it can work without geometric spanners. We demonstrate the technique extends easily to other problems, by showing as an example that it also yields a Gap-ETH-tight approximation scheme for Rectilinear Steiner Tree

Connecting Terminals and 2-Disjoint Connected Subgraphs

Given a graph $G=(V,E)$ and a set of terminal vertices $T$ we say that a superset $S$ of $T$ is $T$-connecting if $S$ induces a connected graph, and $S$ is minimal if no strict subset of $S$ is $T$-connecting. In this paper we prove that there are at most ${|V \setminus T| \choose |T|-2} \cdot 3^{\frac{|V \setminus T|}{3}}$ minimal $T$-connecting sets when $|T| \leq n/3$ and that these can be enumerated within a polynomial factor of this bound. This generalizes the algorithm for enumerating all induced paths between a pair of vertices, corresponding to the case $|T|=2$. We apply our enumeration algorithm to solve the {\sc 2-Disjoint Connected Subgraphs} problem in time $O^*(1.7804^n)$, improving on the recent $O^*(1.933^n)$ algorithm of Cygan et al. 2012 LATIN paper.Comment: 13 pages, 1 figur

From correlation to causation: the cruciality of a collectivity in the context of collective action

This paper discusses a longitudinal field study on collective action which aims to move beyond student samples and enhance mundane realism. First we provide a historical overview of the literature on the what (i.e., antecedents of collective action) and the how (i.e., the methods employed) of the social psychology of protest. This historical overview is substantiated with meta-analytical evidence on how these antecedents and methods changed over time. After the historical overview, we provide an empirical illustration of a longitudinal field study in a natural setting―a newly-built Dutch neighbourhood. We assessed changes in informal embeddedness, efficacy, identification, emotions, and grievances over time. Between t0 and t1 the residents protested against the plan to allow a mosque to carrying out their services in a community building in the neighbourhood. We examined the antecedents of protest before [t0] and after [t1] the protests, and whether residents participated or not. We show how a larger social network functions as a catalyst in steering protest participation. Our longitudinal field study replicates basic findings from experimental and survey research. However, it also shows that one antecedent in particular, which is hard to manipulate in the lab (i.e., the size of someone’s social network), proved to be of great importance. We suggest that in overcoming our most pertinent challenge―causality―we should not only remain in our laboratories but also go out and examine real-life situations with people situated in real-life social networks

Spotting Trees with Few Leaves

We show two results related to the Hamiltonicity and $k$-Path algorithms in undirected graphs by Bj\"orklund [FOCS'10], and Bj\"orklund et al., [arXiv'10]. First, we demonstrate that the technique used can be generalized to finding some $k$-vertex tree with $l$ leaves in an $n$-vertex undirected graph in $O^*(1.657^k2^{l/2})$ time. It can be applied as a subroutine to solve the $k$-Internal Spanning Tree ($k$-IST) problem in $O^*(\min(3.455^k, 1.946^n))$ time using polynomial space, improving upon previous algorithms for this problem. In particular, for the first time we break the natural barrier of $O^*(2^n)$. Second, we show that the iterated random bipartition employed by the algorithm can be improved whenever the host graph admits a vertex coloring with few colors; it can be an ordinary proper vertex coloring, a fractional vertex coloring, or a vector coloring. In effect, we show improved bounds for $k$-Path and Hamiltonicity in any graph of maximum degree $\Delta=4,\ldots,12$ or with vector chromatic number at most 8

Nutrient retention efficiencies in integrated multi-trophic aquaculture

One of the bottlenecks for commercial implementation of integrated multi-trophic aquaculture (IMTA) is the difficulty in quantifying its environmental performance. We reviewed a large body of literature to determine the variability in nutrient dynamics within different IMTA systems (open sea-cages, land-based flow-through and recirculating aquaculture systems), with the aim to provide a generic framework to quantify nutrient retention efficiencies in integrated aquaculture systems. Based on the eco-physiological requirements of the cultured species, as well as the response of “extractive” species to waste from “fed” species, the maximum retention efficiency was defined for a conceptual four-species marine IMTA system (fish–seaweed–bivalve–deposit feeder). This demonstrated that 79%–94% of nitrogen, phosphorus and carbon supplied with fish feed could theoretically be retained. In practice, however, various biological and environmental factors may limit retention efficiencies and thereby influence the bioremediation of IMTA systems. These biological (waste production, stoichiometry in nutrient requirements) and environmental (temporal and spatial connectivity) factors were therefore evaluated against the theoretical reference frame and showed that efficiencies of 45%–75% for closed systems and 40%–50% for open systems are more realistic. This study is thereby the first to provide quantitative estimates for nutrient retention across IMTA systems, demonstrating that a substantial fraction of nutrients released from fish culture units can be retained by extractive species and subsequently harvested. Furthermore, by adapting this framework to the design and the condition prevailing for a specific IMTA system, it becomes a generic tool to analyse the system's bioremediation potential and explore options for further improvement.publishedVersio

Faster space-efficient algorithms for Subset Sum, k -Sum, and related problems

We present randomized algorithms that solve subset sum and knapsack instances with n items in O∗ (20.86n) time, where the O∗ (∙ ) notation suppresses factors polynomial in the input size, and polynomial space, assuming random read-only access to exponentially many random bits. These results can be extended to solve binary integer programming on n variables with few constraints in a similar running time. We also show that for any constant k ≥ 2, random instances of k-Sum can be solved using O(nk -0.5polylog(n)) time and O(log n) space, without the assumption of random access to random bits.Underlying these results is an algorithm that determines whether two given lists of length n with integers bounded by a polynomial in n share a common value. Assuming random read-only access to random bits, we show that this problem can be solved using O(log n) space significantly faster than the trivial O(n2) time algorithm if no value occurs too often in the same list.</p

Space Saving by Dynamic Algebraization

Dynamic programming is widely used for exact computations based on tree decompositions of graphs. However, the space complexity is usually exponential in the treewidth. We study the problem of designing efficient dynamic programming algorithm based on tree decompositions in polynomial space. We show how to construct a tree decomposition and extend the algebraic techniques of Lokshtanov and Nederlof such that the dynamic programming algorithm runs in time $O^*(2^h)$, where $h$ is the maximum number of vertices in the union of bags on the root to leaf paths on a given tree decomposition, which is a parameter closely related to the tree-depth of a graph. We apply our algorithm to the problem of counting perfect matchings on grids and show that it outperforms other polynomial-space solutions. We also apply the algorithm to other set covering and partitioning problems.Comment: 14 pages, 1 figur

A strategy for the characterization of minute chromosome rearrangements using multiple color fluorescence in situ hybridization with chromosome-specific DNA libraries and YAC clones

The identification of marker chromosomes in clinical and tumor cytogenetics by chromosome banding analysis can create problems. In this study, we present a strategy to define minute chromosomal rearrangements by multicolor fluorescence in situ hybridization (FISH) with whole chromosome painting probes derived from chromosome-specific DNA libraries and Alu-polymerase chain reaction (PCR) products of various region-specific yeast artificial chromosome (YAC) clones. To demonstrate the usefulness of this strategy for the characterization of chromosome rearrangements unidentifiable by banding techniques, an 8p+ marker chromosome with two extra bands present in the karyotype of a child with multiple anomalies, malformations, and severe mental retardation was investigated. A series of seven-color FISH experiments with sets of fluorochrome-labeled DNA library probes from flow-sorted chromosomes demonstrated that the additional segment on 8p+ was derived from chromosome 6. For a more detailed characterization of the marker chromosome, three-color FISH experiments with library probes specific to chromosomes 6 and 8 were performed in combination with newly established telomeric and subtelomeric YAC clones from 6q25, 6p23, and 8p23. These experiments demonstrated a trisomy 6pter6p22 and a monosomy 8pter8p23 in the patient. The present limitations for a broad application of this strategy and its possible improvements are discusse