Abstract. Given an undirected graph with positive weights on the vertices, the maximum weight clique problem (MWCP) is to find a subset of mutually adjacent vertices (i.e., a clique) having largest total weight. The problem is known to be NP -hard, even to approximate. Motivated by a recent quadratic programming formulation, which generalizes an earlier remarkable result of Motzkin and Straus, in this paper we propose a new framework for the MWCP based on the corresponding linear complementarity problem (LCP). We show that, generically, all stationary points of the MWCP quadratic program exhibit strict complementarity. Despite this regularity result, however, the LCP turns out to be inherently degenerate, and we find that Lemke's well-known pivoting method, equipped with standard degeneracy resolution strategies, yields unsatisfactory experimental results. We exploit the degeneracy inherent in the problem to develop a variant of Lemke's algorithm which incorporates a new and effective "look-ahead" pivot rule. The resulting algorithm is tested extensively on various instances of random as well as DIMACS benchmark graphs, and the results obtained show the effectiveness of our method.Key words. maximum weight clique, linear complementarity, pivoting methods, quadratic programming, combinatorial optimization, heuristics AMS subject classifications. 90C27, 90C20, 90C33, 90C49, 90C59, 05C69PII. S1052623400381413 1. Introduction. Given an undirected graph, the maximum clique problem (MCP) consists of finding a subset of pairwise adjacent vertices (i.e., a clique) having largest cardinality. The problem is known to be NP -hard for arbitrary graphs and, according to recent theoretical results, so is the problem of approximating it within a constant factor. An important generalization of the MCP arises when positive weights are associated to the vertices of the graph. In this case the problem is known as the maximum weight clique problem (MWCP) and consists of finding a clique in the graph which has largest total weight. (Note that the maximum weight clique does not necessarily have largest cardinality.) It is clear that the classical unweighted version is a special case in which the weights assigned to the vertices are all equal. As an obvious corollary, the MWCP has at least the same computational complexity as its unweighted counterpart. The MWCP has important applications in such fields as computer vision, pattern recognition, and robotics, where weighted graphs are employed as a convenient means of representing high-level pictorial information (see, e.g., [17,28]). We refer to [4] for a recent review concerning algorithms, applications, and complexity issues of this important problem.Inspired by a classical result in graph theory contributed by Motzkin and Straus [24], Gibbons et al. [13] have recently formulated the MWCP in terms of a standard quadratic optimization problem (StQP), which consists of minimizing a quadratic form

Motivated by a recent (continuous) quadratic formulation, in this paper we present a pivoting-based heuristic for graph matching based on the corresponding linear complementarity problem. Experiments are presented which demonstrate the potential of the proposed method.

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Neonatal infections are responsible for 20% of neonatal deaths yearly. In this review, we focused on the origins of the commoner neonatal infections, and we define the role of obstetricians. Regarding group B Streptococcus, a key measure for the prevention of neonatal infection is the vaginal–rectal culture screening at term pregnancy. Intravenous penicillin is the first-line prophylaxis at the start of labor, with intravenous ampicillin as an alternative. First-generation cephalosporins or clindamycin are recommended in case of penicillin allergy. Concerning urinary tract infections (UTIs), guidelines recommend complete urinalysis and urine culture in the first trimester of pregnancy for the screening of asymptomatic bacteriuria. For lower UTIs, guidelines recommend nitrofurantoin as first-choice antibiotic. Amoxicillin or cefalexin are second-line antibiotics. For upper UTIs, guidelines recommend cephalexin per os as first line. Candida spp. colonization affects 20% of pregnant women; however, congenital fetal candidosis and Candida amnionitis are rare. First-line treatment in case of symptomatic vaginitis during pregnancy or asymptomatic colonization during the third trimester is vaginal clotrimazole. Fluconazole is not approved in pregnancy, especially during the first trimester. Genital mycoplasmas colonization during pregnancy is usually asymptomatic and associated with bacterial vaginosis. Colonization is related to neonatal respiratory distress syndrome (RDS), bronchopulmonary dysplasia (BPD), pneumonia, chorioamnionitis, and sepsis. Macrolides are the first-line treatment along with lactobacillus supplementation. In cases of preterm premature rupture of membranes or preterm labor, ceftriaxone, clarithromycin, and metronidazole are required to prevent intra-amniotic infection. Intra-amniotic infection affects 1 to 5% of deliveries at term and one-third of preterm ones and is associated with perinatal death, early-onset neonatal sepsis, RDS, BPD, pneumonia, meningitis, and prematurity-related diseases. Guidelines recommend a combination of ampicillin and gentamicin, and in case of caesarean section, an additional dose of clindamycin or metronidazole is required. In conclusion, obstetricians should be aware that the treatment of maternal infection during pregnancy can prevent potentially lethal infections in the newborn. Key Points