Integrality Gap of the Hypergraphic Relaxation of Steiner Trees: a short proof of a 1.55 upper bound

Recently Byrka, Grandoni, Rothvoss and Sanita (at STOC 2010) gave a 1.39-approximation for the Steiner tree problem, using a hypergraph-based linear programming relaxation. They also upper-bounded its integrality gap by 1.55. We describe a shorter proof of the same integrality gap bound, by applying some of their techniques to a randomized loss-contracting algorithm

Comparative Systematics of Subterranean Amphipod Crustaceans in the Families Crangonyctidae and Bogidiellidae

The research project presented in this doctoral dissertation deals with the systematics of two different taxonomic groups of subterranean amphipods (Crustacea). Therefore, rather than being a single project, this study is divided into several sub-projects. Altogether, the chapters for the sub-projects are composed of five publications. An introductory chapter and a summarizing discussion are added to provide a structural unit for the collection of papers and to compare the results of the individual projects. The thesis investigates the systematics of the amphipod families Bogidiellidae Hertzog, 1936, and Crangonyctidae Bousfield, 1973. Based on descriptive taxonomy according to modern standards, revisions are given for the crangonyctid genus Bactrurus Hay, 1902, the bogidiellid genus Spelaeogammarus da Silva Brum, 1973, and the family Bogidiellidae. The bogidiellid sub-project also includes the description of the new genus and species Megagidiella azul. This study makes an attempt to compile and evaluate molecular and morphological data for two families of gammaridean amphipods. To research the phylogenetic relationships of the Bogidiellidae and Crangonyctidae, cladistic analyses, using external morphological characters, are conducted for each family. In addition, sequence analyses of the 18S (small subunit) rDNA gene are carried out for three species of Bactrurus and several selected amphipod taxa. The results of morphological and molecular analyses are compared and the phylogenetic relationships of the taxa under investigation are discussed, especially emphasizing their biogeographic distribution patterns and current taxonomic classification. In a summarizing chapter, the biogeography and evolutionary history of both families are compared. Moreover, the application of different methods of phylogenetic reconstructions is discussed for the Bogidiellidae and Crangonyctidae, as well as for stygobiont amphipods in general

Sparse dynamic discretization discovery via arc-dependent time discretizations

While many time-dependent network design problems can be formulated as time-indexed formulations with strong relaxations, the size of these formulations depends on the discretization of the time horizon and can become prohibitively large. The recently-developed dynamic discretization discovery (DDD) method allows many time-dependent problems to become more tractable by iteratively solving instances of the problem on smaller networks where each node has its own discrete set of departure times. However, in the current implementation of DDD, all arcs departing a common node share the same set of departure times. This causes DDD to be ineffective for solving problems where all near-optimal solutions require many distinct departure times at the majority of the high-degree nodes in the network. Region-based networks are one such structure that often leads to many high-degree nodes, and their increasing popularity underscores the importance of tailoring solution methods for these networks. To improve methods for solving problems that require many departure times at nodes, we develop a DDD framework where the set of departure times is determined on the arc level rather than the node level. We apply this arc-based DDD method to instances of the service network design problem (SND). We show that an arc-based approach is particularly advantageous when instances arise from region-based networks, and when candidate paths are fixed in the base graph for each commodity. Moreover, our algorithm builds upon the existing DDD framework and achieves these improvements with only benign modifications to the original implementation

Hitting Weighted Even Cycles in Planar Graphs

A classical branch of graph algorithms is graph transversals, where one seeks a minimum-weight subset of nodes in a node-weighted graph G which intersects all copies of subgraphs F from a fixed family F. Many such graph transversal problems have been shown to admit polynomial-time approximation schemes (PTAS) for planar input graphs G, using a variety of techniques like the shifting technique (Baker, J. ACM 1994), bidimensionality (Fomin et al., SODA 2011), or connectivity domination (Cohen-Addad et al., STOC 2016). These techniques do not seem to apply to graph transversals with parity constraints, which have recently received significant attention, but for which no PTASs are known. In the even-cycle transversal (ECT) problem, the goal is to find a minimum-weight hitting set for the set of even cycles in an undirected graph. For ECT, Fiorini et al. (IPCO 2010) showed that the integrality gap of the standard covering LP relaxation is ?(log n), and that adding sparsity inequalities reduces the integrality gap to 10. Our main result is a primal-dual algorithm that yields a 47/7 ? 6.71-approximation for ECT on node-weighted planar graphs, and an integrality gap of the same value for the standard LP relaxation on node-weighted planar graphs

Cladistic Analysis of 37 Mediterranean Bogidiellidae (Amphipoda), Including Bogidiella arista, New Species, From Turkey

A new subterranean amphipod species, Bogidiella (Medigidiella) arista, found in the mesopsam mic ground waters of southern Anatolia, Turkey, is described, together with Bogidiella (Bogidiella) calicali Karaman, the latter being recorded for the first time in the eastern Mediterranean. A cladistic analysis of 37 Mediterranean species of the family Bogidiellidae is performed, using 4 species from the Canary Islands as an outgroup. Alternatively, 2 cladistic software packages, PAUP 3.1.1 and HENNIG86, are employed to calculate consensus trees of minimal length. The resulting trees show more or less identical robust clades, characterizing a central, a central-eastern, and an eastern Mediterranean group. Apart from this pattern of major geographical clusters, all species of the subgenus Medigidiella appear as a robust, monophyletic clade as well. This initial attempt to analyze the phylogeny of Mediterranean bogidiellids forms a useful basis for further, extended studies, using either different outgroup taxa or additional morphological data