An approximation algorithm for a generalized assignment problem with small resource requirements.

We investigate a generalized assignment problem where the resource requirements are either 1 or 2. This problem is motivated by a question that arises when data blocks are to be retrieved from parallel disks as efficiently as possible. The resulting problem is to assign jobs to machines with a given capacity, where each job takes either one or two units of machine capacity, and must satisfy certain assignment restrictions, such that total weight of the assigned jobs is maximized. We derive a 2/3-approximation result for this problem based on relaxing a formulation of the problem so that the resulting constraint matrix is totally unimodular. Further, we prove that the LP-relaxation of a special case of the problem is half-integral, and we derive a weak persistency property.Assignment; Constraint; Data; Matrix; Requirements;

Auction-based Task Allocation for Safe and Energy Efficient UAS Parcel Transportation

In this paper, two greedy auction-based algorithms are proposed for the allocation of heterogeneous tasks to a heterogeneous fleet of UAVs. The tasks set is composed of parcel delivery tasks and charge tasks, the latter to guarantee service persistency. An optimization problem is solved by each agent to determine its bid for each task. When considering delivery tasks, the bidder aims at minimizing the energy consumption, while the minimization of the flight time is adopted for charge tasks bids. The algorithms include a path planner that computes the minimum risk path for each task-UAV bid exploiting a 2D risk map of the operational area, defined in an urban environment. Each solution approach is implemented by means of two auction strategies: single-item and multiple-item. Considerations about complexity and efficiency of the algorithms are drawn from Monte Carlo simulations

Optimum matchings in weighted bipartite graphs

Given an integer weighted bipartite graph $\{G=(U\sqcup V, E), w:E\rightarrow \mathbb{Z}\}$ we consider the problems of finding all the edges that occur in some minimum weight matching of maximum cardinality and enumerating all the minimum weight perfect matchings. Moreover, we construct a subgraph $G_{cs}$ of $G$ which depends on an $\epsilon$-optimal solution of the dual linear program associated to the assignment problem on $\{G,w\}$ that allows us to reduced this problems to their unweighed variants on $G_{cs}$. For instance, when $G$ has a perfect matching and we have an $\epsilon$-optimal solution of the dual linear program associated to the assignment problem on $\{G,w\}$, we solve the problem of finding all the edges that occur in some minimum weight perfect matching in linear time on the number of edges. Therefore, starting from scratch we get an algorithm that solves this problem in time $O(\sqrt{n}m\log(nW))$, where $n=|U|\geq |V|$, $m=|E|$, and $W={\rm max}\{|w(e)|\, :\, e\in E\}$.Comment: 11 page

Safe solutions for walks on graphs

In this thesis we study the concept of “safe solutions” in different problems whose solutions are walks on graphs. A safe solution to a problem X can be understood as a partial solution common to all solutions to problem X. In problems whose solutions are walks on graphs, safe solutions refer to walks common to all walks which are solutions to the problem. In this thesis, we focused on formulating four main graph traversal problems and finding characterizations for those walks contained in all their solutions. We give formulations for these graph traversal problems, we prove some of their combinatorial and structural properties, and we give safe and complete algorithms for finding their safe solutions based on their characterizations. We use the genome assembly problem and its applications as our main motivating example for finding safe solutions in these graph traversal problems. We begin by motivating and exemplifying the notion of safe solutions through a problem on s-t paths in undirected graphs with at least two non-trivial biconnected components S and T and with s ∈ S, t ∈ T . We continue by reviewing similar and related notions in other fields, especially in combinatorial optimization and previous work on the bioinformatics problem of genome assembly. We then proceed to characterize the safe solutions to the Eulerian cycle problem, where one must find a circular walk in a graph G which traverses each edge exactly once. We suggest a characterization for them by improving on (Nagarajan, Pop, JCB 2009) and a polynomial-time algorithm for finding them. We then study edge-covering circular walks in a graph G. We look at the characterization from (Tomescu, Medvedev, JCB 2017) for their safe solutions and their suggested polynomial-time algorithm and we show an optimal O(mn)-time algorithm that we proposed in (Cairo et al. CPM 2017). Finally, we generalize this to edge-covering collections of circular walks. We characterize safe solutions in an edge-covering setting and provide a polynomial-time algorithm for computing them. We suggested these originally in (Obscura et al. ALMOB 2018)

CERN Storage Systems for Large-Scale Wireless

The project aims at evaluating the use of CERN computing infrastructure for next generation sensor networks data analysis. The proposed system allows the simulation of a large-scale sensor array for traffic analysis, streaming data to CERN storage systems in an efficient way. The data are made available for offline and quasi-online analysis, enabling both long term planning and fast reaction on the environment

Ricardian Equivalence Proposition in a NK DSGE Model for two Large Economies: The EU and the US

This paper examines the macroeconomic effects of active fiscal policy management coupled with a monetary policy that follows the Taylor principle. The objective is to investigate the relevance of the Ricardian Equivalence Proposition (REP) in a framework where two large open economies interact and a fraction of the consumers is financially constrained. According to an estimated vector autoregressive model, a positive shock in government expenditure leads to an increase in private consumption (at odds with the permanent income hypothesis). The channels are studied in a fully microfounded dynamic stochastic general equilibrium model economy calibrated for the Euro Area (EU-12) and for the United States. The crucial parameter that drives the break of the REP is the share of financially constrained consumers. Firms produce tradable varieties in a monopolistic competition framework and pricing is à la Calvo, which leads to nominal price stickiness. Labor varieties are immobile across countries and are demanded in an aggregated fashion by firms. Fiscal policy is specified as a time-consistent rule. We simulate through impulseresponse functions parameterizations that yield results consistent with the REP, and estimate a subset of deep parameters employing Bayesian techniques.