Fast reoptimization for the minimum spanning tree problem

AbstractWe study reoptimization versions of the minimum spanning tree problem. The reoptimization setting can generally be formulated as follows: given an instance of the problem for which we already know some optimal solution, and given some “small” perturbations on this instance, is it possible to compute a new (optimal or at least near-optimal) solution for the modified instance without ex nihilo computation? We focus on two kinds of modifications: node-insertions and node-deletions. When k new nodes are inserted together with their incident edges, we mainly propose a fast strategy with complexity O(kn) which provides a max{2,3−(2/(k−1))}-approximation ratio, in complete metric graphs and another one that is optimal with complexity O(nlogn). On the other hand, when k nodes are deleted, we devise a strategy which in O(n) achieves approximation ratio bounded above by 2⌈|Lmax|/2⌉ in complete metric graphs, where Lmax is the longest deleted path and |Lmax| is the number of its edges. For any of the approximation strategies, we also provide lower bounds on their approximation ratios

The Maximum Duo-Preservation String Mapping Problem with Bounded Alphabet

Given two strings A and B such that B is a permutation of A, the max duo-preservation string mapping (MPSM) problem asks to find a mapping ? between them so as to preserve a maximum number of duos. A duo is any pair of consecutive characters in a string and it is preserved by ? if its two consecutive characters in A are mapped to same two consecutive characters in B. This problem has received a growing attention in recent years, partly as an alternative way to produce approximation algorithms for its minimization counterpart, min common string partition, a widely studied problem due its applications in comparative genomics. Considering this favored field of application with short alphabet, it is surprising that MPSM^?, the variant of MPSM with bounded alphabet, has received so little attention, with a single yet impressive work that provides a 2.67-approximation achieved in O(n) [Brubach, 2018], where n = |A| = |B|. Our work focuses on MPSM^?, and our main contribution is the demonstration that this problem admits a Polynomial Time Approximation Scheme (PTAS) when ? = O(1). We also provide an alternate, somewhat simpler, proof of NP-hardness for this problem compared with the NP-hardness proof presented in [Haitao Jiang et al., 2012]

Graph médian généralisé via des minimisations alternées.

International audienceComputing a graph prototype may constitute a core element for clustering or classification tasks. However, its computation is an NP-Hard problem, even for simple classes of graphs. In this paper, we propose an efficient approach based on block coordinate descent to compute a generalized median graph from a set of graphs. This approach relies on a clear definition of the optimization process and handles labeling on both edges and nodes. This iterative process optimizes the edit operations to perform on a graph alternatively on nodes and edges. Several experiments on different datasets show the efficiency of our approach.Calculer un graphe prototype peut constituer une étape centrale pour des méthodes de clustering ou de classification. Toutefois, ce calcul est NP-difficile même pour des classes de graphes simples. Nous proposons dans ce papier une approche efficace basée sur une minimisation alternée pour calculer le graphe médian d'un ensemble. Cette approche s'appuie sur une définition claire du processus d'optimisation et inclue l'étiquetage à la fois des nœuds et des arêtes. Ce processus itératif optimise les opérations à effectuer alternativement sur les sommets et les arêtes. Plusieurs expériences sur des jeux de données différents montrent l'efficacité de notre approche

On the probabilistic min spanning tree Problem

We study a probabilistic optimization model for min spanning tree, where any vertex vi of the input-graph G(V,E) has some presence probability pi in the final instance G′ ⊂ G that will effectively be optimized. Suppose that when this “real” instance G′ becomes known, a spanning tree T, called anticipatory or a priori spanning tree, has already been computed in G and one can run a quick algorithm (quicker than one that recomputes from scratch), called modification strategy, that modifies the anticipatory tree T in order to fit G ′. The goal is to compute an anticipatory spanning tree of G such that, its modification for any G ′ ⊆ G is optimal for G ′. This is what we call probabilistic min spanning tree problem. In this paper we study complexity and approximation of probabilistic min spanning tree in complete graphs under two distinct modification strategies leading to different complexity results for the problem. For the first of the strategies developed, we also study two natural subproblems of probabilistic min spanning tree, namely, the probabilistic metric min spanning tree and the probabilistic min spanning tree 1,2 that deal with metric complete graphs and complete graphs with edge-weights either 1, or 2, respectively

Characterisation of secreted exosomes from the intestinal nematode Heligmosomoides polygyrus

The parasite secretome has been shown to play a key role in both pathogenicity and the regulation of host defence, allowing pathogens, such as helminths, to establish a chronic infection within the host. The recently discovered presence of extracellular vesicles within parasite-derived excretory-secretory products introduces a new mechanism of potential cross-species communication. Extracellular vesicles (EVs), such as exosomes, facilitate cellular communication through the transfer of small RNAs, lipids and proteins between cells and organisms across all three kingdoms of life. In addition to their roles in normal physiology, EVs also transport molecules from pathogens to hosts, presenting parasite antigens and transferring infectious agents. Here, I examine secreted vesicles from the murine gastrointestinal nematode Heligmosomoides polygyrus, and their potential role in the host-helminth interactions. Transmission electron microscopy reveals vesicle-like structures of 50- 100 nM in the ultracentrifuged secretory product, and potential evidence of multi-vesicular bodies in the worm intestine. This, coupled with information from the exoproteome, helped support the hypothesis that exosomes originate from the parasite intestinal tract. I have completed a series of studies looking at the fundamental properties of exosome-cell interactions, providing comparative studies between mammalian and H. polygyrus-derived exosomes. I have determined some of the key factors influencing exosome uptake, including time of incubation, cell type and exosome origin. Through microarray analysis of H. polygyrus exosome-treated small intestinal epithelial cells, we see significant gene expression changes, including those involved in the regulation of signalling and the immune response, such as DUSP1 (dual-specificity phosphatase) and IL1RL1 (the receptor for IL-33). The modest reduction of inflammatory cytokine responses by exosomes in small intestinal cell lines was amplified in immune cells, such as macrophages. Exosomes can significantly reduce expression of classical activation markers, as well as inflammatory cytokine production in the macrophage cell line RAW 264.7, and this is further supported by similar responses in bone marrow-derived macrophages. Owing to their suppressive nature, I demonstrate that immunization of mice with an exosome/alum conjugate generates significant protection from a subsequent H. polygyrus larval challenge, as seen through a reduction in egg counts and worm burden. I have investigated the role of the IL33 receptor (IL-33R); a key molecule associated with parasitic resistance that is suppressed by exosomes in type-2 associated immune responses. Uptake of H. polygyrus-derived exosomes by alternatively activated macrophages caused the suppression of type 2 cytokine/protein release and the reduction of key genes associated with this phenotype. In addition, there was also significant repression of both transcript and surface T1/ST2, a subunit of the IL-33R). Using a model of lung inflammation, in vivo studies demonstrate that, in both prophylactic and co-administration experiments, exosomes modulate the innate cellular response. This is represented by changes in the number of innate lymphoid cells (ILCs), bronchoalveolar lavage eosinophils and type-2 cytokine output. In this system, the expression of T1/ST2 on type 2 ILCs was also significantly reduced. I have extended the investigation on exosome-IL-33R responses by using T1/ST2 knockout mice. Despite generating strong antibody responses, vaccination against exosomes could not protect T1/ST2 knockout mice against a subsequent infection. This work suggests that exosomes secreted by nematodes could mediate the transfer and uptake of parasite products into host cells, establishing cross-species communication to suppress the host ‘danger’ or inflammatory response

A survey on combinatorial optimization in dynamic environments

This survey presents major results and issues related to the study of NPO problems in dynamic environments, that is, in settings where instances are allowed to undergo some modifications over time. In particular, the survey focuses on two complementary frameworks. The first one is the reoptimization framework, where an instance I that is already solved undergoes some local perturbation. The goal is then to make use of the information provided by the initial solution to compute a new solution. The second framework is probabilistic optimization, where the instance to optimize is not fully known at the time when a solution is to be proposed, but results from a determined Bernoulli process. Then, the goal is to compute a solution with optimal expected value

Optimization in dynamic environments

This survey presents major results and issues related to the study of NPO problems in dynamic environments, that is, in settings where instances are allowed to undergo some modifications over time. In particular, the survey focuses on two complementary frameworks. The first one is the reoptimization framework, where an instance I that is already solved undergoes some local perturbation. The goal is then to make use of the information provided by the initial solution to compute a new solution. The second framework is probabilistic optimization, where the instance to optimize is not fully known at the time when a solution is to be proposed, but results from a determined Bernoulli process. Then, the goal is to compute a solution with optimal expected value

Exponential approximation schemata for some network design problems

International audienceWe study approximation of some well-known network design problems such as traveling salesman problem (for both minimization and maximization versions) and min steiner tree, by moderately exponential algorithms. The general goal of the issue of moderately exponential approximationis to catch-up on polynomial inapproximability, by providing algorithms achieving, with worst-caserunning times importantly smaller than those needed for exact computation, approximation ratiosunachievable in polynomial time

Fréchet Mean Computation in Graph Space through Projected Block Gradient Descent

International audienceA fundamental concept in statistics is the concept of Fréchet sample mean. While its computation is a simple task in Euclidian space, the same does not hold for less structured spaces such as the space of graphs, where concepts of distance or mid-point can be hard to compute. We present some work in progress regarding new distance measures and new algorithms to compute the Fréchet mean in the space of Graphs