Utilitarian Mechanism Design for Multiobjective Optimization

In a classic optimization problem, the complete input data is assumed to be known to the algorithm. This assumption may not be true anymore in optimization problems motivated by the Internet where part of the input data is private knowledge of independent selfish agents. The goal of algorithmic mechanism design is to provide (in polynomial time) a solution to the optimization problem and a set of incentives for the agents such that disclosing the input data is a dominant strategy for the agents. In the case of NP-hard problems, the solution computed should also be a good approximation of the optimum. In this paper we focus on mechanism design for multiobjective optimization problems. In this setting we are given a main objective function and a set of secondary objectives which are modeled via budget constraints. Multiobjective optimization is a natural setting for mechanism design as many economical choices ask for a compromise between different, partially conflicting goals. The main contribution of this paper is showing that two of the main tools for the design of approximation algorithms for multiobjective optimization problems, namely, approximate Pareto sets and Lagrangian relaxation, can lead to truthful approximation schemes. By exploiting the method of approximate Pareto sets, we devise truthful deterministic and randomized multicriteria fully polynomial-time approximation schemes (FPTASs) for multiobjective optimization problems whose exact version admits a pseudopolynomial-time algorithm, as, for instance, the multibudgeted versions of minimum spanning tree, shortest path, maximum (perfect) matching, and matroid intersection. Our construction also applies to multidimensional knapsack and multiunit combinatorial auctions. Our FPTASs compute a $(1+\varepsilon)$-approximate solution violating each budget constraint by a factor $(1+\varepsilon)$. When feasible solutions induce an independence system, i.e., when subsets of feasible solutions are feasible as well, we present a PTAS (not violating any constraint), which combines the approach above with a novel monotone way to guess the heaviest elements in the optimum solution. Finally, we present a universally truthful Las Vegas PTAS for minimum spanning tree with a single budget constraint, where one wants to compute a minimum cost spanning tree whose length is at most a given value $L$. This result is based on the Lagrangian relaxation method, in combination with our monotone guessing step and with a random perturbation step (ensuring low expected running time). This result can be derandomized in the case of integral lengths. All the mentioned results match the best known approximation ratios, which are, however, obtained by nontruthful algorithms

simultaneous cycle sequencing assessment of tg m and tn tract length in cftr gene

The lengths of the dinucleotide (TG) m and mononucleotide T n repeats, both located at the intron 8/exon 9 splice acceptor site of the cystic fibrosis transmembrane conductance regulator (CFTR) gene whose mutations cause cystic fibrosis (CF), have been shown to influence the skipping of exon 9 in CFTR mRNA. This exon 9-skipped mRNA encodes a nonfunctional protein and is associated with various clinical manifestations in CF. As a result of growing interest in these repeats, several assessment methods have been developed, most of which are, however, cumbersome, multi-step, and time consuming. Here, we describe a rapid method for the simultaneous assessment of the lengths of both (TG) m and T n repeats, based on a nonradioactive cycle sequencing procedure that can be performed even without DNA extraction. This method determines the lengths of the (TG) m and T n tracts of both alleles, which in our samples ranged from TG 8 to TG 12 in the presence of T 5 , T 7 , and T 9 alleles, and also fully assesses the aplotypes. In addition, the repeats in the majority of these samples can be assessed by single-strand sequencing, with no need to sequence the other strand, thereby saving to sequence the other strand, thereby saving a considerable amount of time and effort

Set covering with our eyes closed

Given a universe $U$ of $n$ elements and a weighted collection $\mathscr{S}$ of $m$ subsets of $U$, the universal set cover problem is to a priori map each element $u \in U$ to a set $S(u) \in \mathscr{S}$ containing $u$ such that any set $X{\subseteq U}$ is covered by S(X)=\cup_{u\in XS(u). The aim is to find a mapping such that the cost of $S(X)$ is as close as possible to the optimal set cover cost for $X$. (Such problems are also called oblivious or a priori optimization problems.) Unfortunately, for every universal mapping, the cost of $S(X)$ can be $\Omega(\sqrt{n})$ times larger than optimal if the set $X$ is adversarially chosen. In this paper we study the performance on average, when $X$ is a set of randomly chosen elements from the universe: we show how to efficiently find a universal map whose expected cost is $O(\log mn)$ times the expected optimal cost. In fact, we give a slightly improved analysis and show that this is the best possible. We generalize these ideas to weighted set cover and show similar guarantees to (nonmetric) facility location, where we have to balance the facility opening cost with the cost of connecting clients to the facilities. We show applications of our results to universal multicut and disc-covering problems and show how all these universal mappings give us algorithms for the stochastic online variants of the problems with the same competitive factors

Matroid and Knapsack Center Problems

In the classic $k$-center problem, we are given a metric graph, and the objective is to open $k$ nodes as centers such that the maximum distance from any vertex to its closest center is minimized. In this paper, we consider two important generalizations of $k$-center, the matroid center problem and the knapsack center problem. Both problems are motivated by recent content distribution network applications. Our contributions can be summarized as follows: 1. We consider the matroid center problem in which the centers are required to form an independent set of a given matroid. We show this problem is NP-hard even on a line. We present a 3-approximation algorithm for the problem on general metrics. We also consider the outlier version of the problem where a given number of vertices can be excluded as the outliers from the solution. We present a 7-approximation for the outlier version. 2. We consider the (multi-)knapsack center problem in which the centers are required to satisfy one (or more) knapsack constraint(s). It is known that the knapsack center problem with a single knapsack constraint admits a 3-approximation. However, when there are at least two knapsack constraints, we show this problem is not approximable at all. To complement the hardness result, we present a polynomial time algorithm that gives a 3-approximate solution such that one knapsack constraint is satisfied and the others may be violated by at most a factor of $1+\epsilon$. We also obtain a 3-approximation for the outlier version that may violate the knapsack constraint by $1+\epsilon$.Comment: A preliminary version of this paper is accepted to IPCO 201

A simplified analytical model of ultrafine particle concentration within an indoor environment

Exposure to indoor fine and ultrafine particulate matter (PM) has been recognised as a fundamental problem as most people spend over 85% of their time indoor. Experimental data derived from a field campaign conducted in a confined environment have been used to investigate the physical mechanisms governing indoor-outdoor PM exchanges in different operating conditions, e.g. natural ventilation and infiltration. An analytical model based on the mass balance of PM has been used to estimate indoor fine and ultrafine PM concentration. Indoor-outdoor concentration ratio, penetration factor and air exchange rate have been estimated and related to the differential pressure measured at the openings

On the Complexity of the Asymmetric VPN Problem

We give the first constant factor approximation algorithm for the asymmetric Virtual Private Network (VPN) problem with arbitrary concave costs. We even show the stronger result, that there is always a tree solution of cost at most 2 OPT and that a tree solution of (expected) cost at most 49.84 OPT can be determined in polynomial time. Furthermore, we answer an outstanding open question about the complexity status of the so called balanced VPN problem by proving its NP-hardness

Analysis of new control applications

This document reports the results of the activities performed during the first year of the CRUTIAL project, within the Work Package 1 "Identification and description of Control System Scenarios". It represents the outcome of the analysis of new control applications in the Power System and the identification of critical control system scenarios to be explored by the CRUTIAL project

Spotting Trees with Few Leaves

We show two results related to the Hamiltonicity and $k$-Path algorithms in undirected graphs by Bj\"orklund [FOCS'10], and Bj\"orklund et al., [arXiv'10]. First, we demonstrate that the technique used can be generalized to finding some $k$-vertex tree with $l$ leaves in an $n$-vertex undirected graph in $O^*(1.657^k2^{l/2})$ time. It can be applied as a subroutine to solve the $k$-Internal Spanning Tree ($k$-IST) problem in $O^*(\min(3.455^k, 1.946^n))$ time using polynomial space, improving upon previous algorithms for this problem. In particular, for the first time we break the natural barrier of $O^*(2^n)$. Second, we show that the iterated random bipartition employed by the algorithm can be improved whenever the host graph admits a vertex coloring with few colors; it can be an ordinary proper vertex coloring, a fractional vertex coloring, or a vector coloring. In effect, we show improved bounds for $k$-Path and Hamiltonicity in any graph of maximum degree $\Delta=4,\ldots,12$ or with vector chromatic number at most 8

Multiple small RNAs identified in Mycobacterium bovis BCG are also expressed in Mycobacterium tuberculosis and Mycobacterium smegmatis

Tuberculosis (TB) is a major global health problem, infecting millions of people each year. The causative agent of TB, Mycobacterium tuberculosis, is one of the world’s most ancient and successful pathogens. However, until recently, no work on small regulatory RNAs had been performed in this organism. Regulatory RNAs are found in all three domains of life, and have already been shown to regulate virulence in well-known pathogens, such as Staphylococcus aureus and Vibrio cholera. Here we report the discovery of 34 novel small RNAs (sRNAs) in the TB-complex M. bovis BCG, using a combination of experimental and computational approaches. Putative homologues of many of these sRNAs were also identified in M. tuberculosis and/or M. smegmatis. Those sRNAs that are also expressed in the non-pathogenic M. smegmatis could be functioning to regulate conserved cellular functions. In contrast, those sRNAs identified specifically in M. tuberculosis could be functioning in mediation of virulence, thus rendering them potential targets for novel antimycobacterials. Various features and regulatory aspects of some of these sRNAs are discussed