Improved Approximation Algorithms for Box Contact Representations ⋆

Abstract. We study the following geometric representation problem: Given a graph whose vertices correspond to axis-aligned rectangles with fixed dimensions, arrange the rectangles without overlaps in the plane such that two rectangles touch if the graph contains an edge between them. This problem is called CONTACT REPRESENTATION OF WORD NETWORKS (CROWN) since it formalizes the geometric problem behind drawing word clouds in which semantically related words are close to each other. CROWN is known to be NP-hard, and there are approximation algorithms for certain graph classes for the optimization version, MAX-CROWN, in which realizing each desired adjacency yields a certain profit. We present the first O(1)-approximation algorithm for the general case, when the input is a complete weighted graph, and for the bipartite case. Since the subgraph of realized adjacencies is necessarily planar, we also consider several planar graph classes (namely stars, trees, outerplanar, and planar graphs), improving upon the known results. For some graph classes, we also describe improvements in the unweighted case, where each adjacency yields the same profit. Finally, we show that the problem is APX-hard on bipartite graphs of bounded maximum degree.

Combinatorial Auctions without Money

Algorithmic Mechanism Design attempts to marry computation and incentives, mainly by leveraging monetary transfers between designer and selfish agents involved. This is principally because in absence of money, very little can be done to enforce truthfulness. However, in certain applications, money is unavailable, morally unacceptable or might simply be at odds with the objective of the mechanism. For example, in Combinatorial Auctions (CAs), the paradigmatic problem of the area, we aim at solutions of maximum social welfare, but still charge the society to ensure truthfulness. We focus on the design of incentive-compatible CAs without money in the general setting of k-minded bidders. We trade monetary transfers with the observation that the mechanism can detect certain lies of the bidders: i.e., we study truthful CAs with verification and without money. In this setting, we characterize the class of truthful mechanisms and give a host of upper and lower bounds on the approximation ratio obtained by either deterministic or randomized truthful mechanisms. Our results provide an almost complete picture of truthfully approximating CAs in this general setting with multi-dimensional bidders

Prevalence of pathogenic BRCA1/2 germline mutations among 802 women with unilateral triple-negative breast cancer without family cancer history

Background: There is no international consensus up to which age women with a diagnosis of triple-negative breast cancer (TNBC) and no family history of breast or ovarian cancer should be offered genetic testing for germline BRCA1 and BRCA2 (gBRCA) mutations. Here, we explored the association of age at TNBC diagnosis with the prevalence of pathogenic gBRCA mutations in this patient group. Methods: The study comprised 802 women (median age 40 years, range 19–76) with oestrogen receptor, progesterone receptor, and human epidermal growth factor receptor type 2 negative breast cancers, who had no relatives with breast or ovarian cancer. All women were tested for pathogenic gBRCA mutations. Logistic regression analysis was used to explore the association between age at TNBC diagnosis and the presence of a pathogenic gBRCA mutation. Results: A total of 127 women with TNBC (15.8%) were gBRCA mutation carriers (BRCA1: n = 118, 14.7%; BRCA2: n = 9, 1.1%). The mutation prevalence was 32.9% in the age group 20–29 years compared to 6.9% in the age group 60–69 years. Logistic regression analysis revealed a significant increase of mutation frequency with decreasing age at diagnosis (odds ratio 1.87 per 10 year decrease, 95%CI 1.50–2.32, p < 0.001). gBRCA mutation risk was predicted to be > 10% for women diagnosed below approximately 50 years. Conclusions: Based on the general understanding that a heterozygous mutation probability of 10% or greater justifies gBRCA mutation screening, women with TNBC diagnosed before the age of 50 years and no familial history of breast and ovarian cancer should be tested for gBRCA mutations. In Germany, this would concern approximately 880 women with newly diagnosed TNBC per year, of whom approximately 150 are expected to be identified as carriers of a pathogenic gBRCA mutation

Computational identification of gene–social environment interaction at the human IL6 locus

To identify genetic factors that interact with social environments to impact human health, we used a bioinformatic strategy that couples expression array–based detection of environmentally responsive transcription factors with in silico discovery of regulatory polymorphisms to predict genetic loci that modulate transcriptional responses to stressful environments. Tests of one predicted interaction locus in the human IL6 promoter (SNP rs1800795) verified that it modulates transcriptional response to β-adrenergic activation of the GATA1 transcription factor in vitro. In vivo validation studies confirmed links between adverse social conditions and increased transcription of GATA1 target genes in primary neural, immune, and cancer cells. Epidemiologic analyses verified the health significance of those molecular interactions by documenting increased 10-year mortality risk associated with late-life depressive symptoms that occurred solely for homozygous carriers of the GATA1-sensitive G allele of rs1800795. Gating of depression-related mortality risk by IL6 genotype pertained only to inflammation-related causes of death and was associated with increased chronic inflammation as indexed by plasma C-reactive protein. Computational modeling of molecular interactions, in vitro biochemical analyses, in vivo animal modeling, and human molecular epidemiologic analyses thus converge in identifying β-adrenergic activation of GATA1 as a molecular pathway by which social adversity can alter human health risk selectively depending on individual genetic status at the IL6 locus