Dynamic Matching Market Design

We introduce a simple benchmark model of dynamic matching in networked markets, where agents arrive and depart stochastically and the network of acceptable transactions among agents forms a random graph. We analyze our model from three perspectives: waiting, optimization, and information. The main insight of our analysis is that waiting to thicken the market can be substantially more important than increasing the speed of transactions, and this is quite robust to the presence of waiting costs. From an optimization perspective, naive local algorithms, that choose the right time to match agents but do not exploit global network structure, can perform very close to optimal algorithms. From an information perspective, algorithms that employ even partial information on agents' departure times perform substantially better than those that lack such information. To elicit agents' departure times, we design an incentive-compatible continuous-time dynamic mechanism without transfers

The blind men and the elephant: Integrated offline/online optimization under uncertainty

open3noOptimization problems under uncertainty are traditionally solved either via offline or online methods. Offline approaches can obtain high-quality robust solutions, but have a considerable computational cost. Online algorithms can react to unexpected events once they are observed, but often run under strict time constraints, preventing the computation of optimal solutions. Many real world problems, however, have both offline and online elements: a substantial amount of time and information is frequently available (offline) before an online problem is solved (e.g. energy production forecasts, or historical travel times in routing problems); in other cases both offline (i.e. strategic) and online (i.e. operational) decisions need to be made. Surprisingly, the interplay of these offline and online phases has received little attention: like in the blind men and the elephant tale, we risk missing the whole picture, and the benefits that could come from integrated offline/online optimization. In this survey we highlight the potential shortcomings of pure methods when applied to mixed offline/online problems, we review the strategies that have been designed to take advantage of this integration, and we suggest directions for future research.openDe Filippo A.; Lombardi M.; Milano M.De Filippo A.; Lombardi M.; Milano M

Improved Approximation Algorithms for Stochastic Matching

In this paper we consider the Stochastic Matching problem, which is motivated by applications in kidney exchange and online dating. We are given an undirected graph in which every edge is assigned a probability of existence and a positive profit, and each node is assigned a positive integer called timeout. We know whether an edge exists or not only after probing it. On this random graph we are executing a process, which one-by-one probes the edges and gradually constructs a matching. The process is constrained in two ways: once an edge is taken it cannot be removed from the matching, and the timeout of node $v$ upper-bounds the number of edges incident to $v$ that can be probed. The goal is to maximize the expected profit of the constructed matching. For this problem Bansal et al. (Algorithmica 2012) provided a $3$-approximation algorithm for bipartite graphs, and a $4$-approximation for general graphs. In this work we improve the approximation factors to $2.845$ and $3.709$, respectively. We also consider an online version of the bipartite case, where one side of the partition arrives node by node, and each time a node $b$ arrives we have to decide which edges incident to $b$ we want to probe, and in which order. Here we present a $4.07$-approximation, improving on the $7.92$-approximation of Bansal et al. The main technical ingredient in our result is a novel way of probing edges according to a random but non-uniform permutation. Patching this method with an algorithm that works best for large probability edges (plus some additional ideas) leads to our improved approximation factors

Matching with Commitments

We consider the following stochastic optimization problem first introduced by Chen et al. in \cite{chen}. We are given a vertex set of a random graph where each possible edge is present with probability p_e. We do not know which edges are actually present unless we scan/probe an edge. However whenever we probe an edge and find it to be present, we are constrained to picking the edge and both its end points are deleted from the graph. We wish to find the maximum matching in this model. We compare our results against the optimal omniscient algorithm that knows the edges of the graph and present a 0.573 factor algorithm using a novel sampling technique. We also prove that no algorithm can attain a factor better than 0.898 in this model

Hydrophilic interaction chromatography – mass spectrometry for metabolomics and proteomics:state-of-the-art and current trends

Among all the –omics approaches, proteomics and metabolomics have received increased attention over the last decade. Both approaches have reached a certain level of maturity, showing their relevance in numerous clinical applications, including biomarkers discovery, improved diagnosis, staging, and prognosis of diseases, as well as a better knowledge on various (patho-)physiological processes. Analytically, reversed-phase liquid chromatography – mass spectrometry (RPLC-MS) is considered the golden standard in proteomics and metabolomics, due to its ease of use and reproducilibity. However, RPLC-MS alone is not sufficient to resolve the complexity of the proteome, while very polar metabolites are typically poorly retained. In this context, hydrophilic interaction chromatography (HILIC) represents an attractive complementary approach, due to its orthogonal separation mechanism. This review presents an overview of the literature reporting the application of HILIC-MS in metabolomics and proteomics. For metabolomics the focus is on the analysis of bioactive lipids, amino acids, organic acids, and nucleotides/nucleosides, whereas for proteomics the analysis of complex samples and protein post-translational modifications therein using bottom-up, middle up/down proteomics and intact protein analysis is discussed. The review handles the technological aspects related to the use of HILIC-MS in both proteomics and metabolomics, paying attention to stationary phases, mobile phase conditions, injection volume and column temperature. Recent trends and developments in the application of HILIC-MS in proteomics and metabolomics are also presented and discussed, highlighting the advantages the technique can provide in addition or complementary to RPLC-MS, as well as the current limitations and possible solutions