On the Enumeration of Minimal Covers and Minimal Forbidden Sets

An independence system is a family I of subsets of a ground set V with the property that any subset of any member of I also belongs to I. The inclusion-minimal sets not in I are called minimal covers. We prove several complexity results related to computation, enumeration, and counting of the minimal covers of an independence system. Our motivation to study these problems is their importance in the solution of resource-constrained scheduling problems. There the minimal covers correspond to minimal subsets of jobs that must not be scheduled simultaneously, so-called minimal forbidden sets. In this context, minimal covers are the minimal infeasible 0/1-solutions of a linear inequality system. We propose and analyze a simple backtracking algorithm that generates a complete representation of all minimal covers of the independence system induced by a linear inequality system. The practical performance of this algorithm is evaluated on the basis of instances from the project scheduling library PSPLIB.computer science applications;

Fast Ejection Chain Algorithms for Vehicle Routing with Time Windows

This paper introduces new ejection chain strategies to effectively target vehicle routing problems with time window constraints (VRPTW). Ejection chain procedures are based on the idea of compound moves that allow a variable number of solution components to be modified within any single iteration of a local search algorithm. The yardstick behind such procedures is the underlying reference structure, which is the structure that is used to coordinate the moves that are available for the local search algorithm. The main contribution of the paper is a new reference structure that is particularly suited in order to handle the asymmetric aspects in a VRPTW. The new reference structure is a generalization of the doubly rooted reference structure introduced by Glover, resulting in a new, powerful neighborhood for the VRPTW. We use tabu search for the generation of the ejection chains. On a higher algorithmic level, we study the effect of different meta heuristics to steer the tabu chain ejection process. Computational results confirm that our approach leads to very fast algorithms that can compete with the current state of the art algorithms for the VRPTW.operations research and management science;

Pricing bridges to cross a river.

We consider a Stackelberg pricing problem in directed, uncapacitated networks. Tariffs have to be defined by an operator, the leader, for a subset of m arcs, the tariff arcs. Costs of all other arcs are assumed to be given. There are n clients, the followers, that route their demand independent of each other on paths with minimal total cost. The problem is to find tariffs that maximize the operator's revenue. Motivated by problems in telecommunication networks, we consider a restricted version of this problem, assuming that each client utilizes at most one of the operator's tariff arcs. The problem is equivalent to pricing bridges that clients can use in order to cross a river. We prove that this problem is APX-hard. Moreover, we show that uniform pricing yields both an m–approximation, and a (1 + lnD)–approximation. Here, D is upper bounded by the total demand of all clients. We furthermore discuss some polynomially solvable special cases, and present a short computational study with instances from France Télécom. In addition, we consider the problem under the additional restriction that the operator must serve all clients. We prove that this problem does not admit approximation algorithms with any reasonable performance guarantee, unless NP = ZPP, and we prove the existence of an n–approximation algorithm.Pricing; Networks; Tariffs; Costs; Cost; Demand; Problems; Order; Yield; Studies; Approximation; Algorithms; Performance;

Predicting protein functions with message passing algorithms

Motivation: In the last few years a growing interest in biology has been shifting towards the problem of optimal information extraction from the huge amount of data generated via large scale and high-throughput techniques. One of the most relevant issues has recently become that of correctly and reliably predicting the functions of observed but still functionally undetermined proteins starting from information coming from the network of co-observed proteins of known functions. Method: The method proposed in this article is based on a message passing algorithm known as Belief Propagation, which takes as input the network of proteins physical interactions and a catalog of known proteins functions, and returns the probabilities for each unclassified protein of having one chosen function. The implementation of the algorithm allows for fast on-line analysis, and can be easily generalized to more complex graph topologies taking into account hyper-graphs, {\em i.e.} complexes of more than two interacting proteins.Comment: 12 pages, 9 eps figures, 1 additional html tabl

Distance, dissimilarity index, and network community structure

We address the question of finding the community structure of a complex network. In an earlier effort [H. Zhou, {\em Phys. Rev. E} (2003)], the concept of network random walking is introduced and a distance measure defined. Here we calculate, based on this distance measure, the dissimilarity index between nearest-neighboring vertices of a network and design an algorithm to partition these vertices into communities that are hierarchically organized. Each community is characterized by an upper and a lower dissimilarity threshold. The algorithm is applied to several artificial and real-world networks, and excellent results are obtained. In the case of artificially generated random modular networks, this method outperforms the algorithm based on the concept of edge betweenness centrality. For yeast's protein-protein interaction network, we are able to identify many clusters that have well defined biological functions.Comment: 10 pages, 7 figures, REVTeX4 forma

A dual function for Pex3p in peroxisome formation and inheritance

Saccharomyces cerevisiae Pex3p has been shown to act at the ER during de novo peroxisome formation. However, its steady state is at the peroxisomal membrane, where its role is debated. Here we show that Pex3p has a dual function: one in peroxisome formation and one in peroxisome segregation. We show that the peroxisome retention factor Inp1p interacts physically with Pex3p in vitro and in vivo, and split-GFP analysis shows that the site of interaction is the peroxisomal membrane. Furthermore, we have generated PEX3 alleles that support peroxisome formation but fail to support recruitment of Inp1p to peroxisomes, and as a consequence are affected in peroxisome segregation. We conclude that Pex3p functions as an anchor for Inp1p at the peroxisomal membrane, and that this function is independent of its role at the ER in peroxisome biogenesis

The evolutionary dynamics of the Saccharomyces cerevisiae protein interaction network after duplication

Gene duplication is an important mechanism in the evolution of protein interaction networks. Duplications are followed by the gain and loss of interactions, rewiring the network at some unknown rate. Because rewiring is likely to change the distribution of network motifs within the duplicated interaction set, it should be possible to study network rewiring by tracking the evolution of these motifs. We have developed a mathematical framework that, together with duplication data from comparative genomic and proteomic studies, allows us to infer the connectivity of the preduplication network and the changes in connectivity over time. We focused on the whole-genome duplication (WGD) event in Saccharomyces cerevisiae. The model allowed us to predict the frequency of intergene interaction before WGD and the post duplication probabilities of interaction gain and loss. We find that the predicted frequency of self-interactions in the preduplication network is significantly higher than that observed in today's network. This could suggest a structural difference between the modern and ancestral networks, preferential addition or retention of interactions between ohnologs, or selective pressure to preserve duplicates of self-interacting proteins

Gecko diversity : a history of global discovery

1935 gecko species (and 224 subspecies) were known in December 2019 in seven families and 124 genera. These nearly 2000 species were described by ~950 individuals of whom more than 100 described more than 10 gecko species each. Most gecko species were discovered during the past 40 years. The primary type specimens of all currently recognized geckos (including subspecies) are distributed over 161 collections worldwide, with 20 collections having about two thirds of all primary types. The primary type specimens of about 40 gecko taxa have been lost or unknown. The phylogeny of geckos is well studied, with DNA sequences being available for ~76% of all geckos (compared to ~63% in other reptiles) and morphological characters now being collected in databases. Geographically, geckos occur on five continents and many islands but are most species-rich in Australasia (which also houses the greatest diversity of family-level taxa), Southeast Asia, Africa, Madagascar, and the West Indies. Among countries, Australia has the highest number of geckos (241 species), with India, Madagascar, and Malaysia being the only other countries with more than 100 described species each. As expected, when correcting for land area, countries outside the tropics have fewer geckos