Enforcing efficient equilibria in network design games via subsidies

The efficient design of networks has been an important engineering task that involves challenging combinatorial optimization problems. Typically, a network designer has to select among several alternatives which links to establish so that the resulting network satisfies a given set of connectivity requirements and the cost of establishing the network links is as low as possible. The Minimum Spanning Tree problem, which is well-understood, is a nice example. In this paper, we consider the natural scenario in which the connectivity requirements are posed by selfish users who have agreed to share the cost of the network to be established according to a well-defined rule. The design proposed by the network designer should now be consistent not only with the connectivity requirements but also with the selfishness of the users. Essentially, the users are players in a so-called network design game and the network designer has to propose a design that is an equilibrium for this game. As it is usually the case when selfishness comes into play, such equilibria may be suboptimal. In this paper, we consider the following question: can the network designer enforce particular designs as equilibria or guarantee that efficient designs are consistent with users' selfishness by appropriately subsidizing some of the network links? In an attempt to understand this question, we formulate corresponding optimization problems and present positive and negative results.Comment: 30 pages, 7 figure

On the Configuration LP for Maximum Budgeted Allocation

We study the Maximum Budgeted Allocation problem, i.e., the problem of selling a set of $m$ indivisible goods to $n$ players, each with a separate budget, such that we maximize the collected revenue. Since the natural assignment LP is known to have an integrality gap of $\frac{3}{4}$, which matches the best known approximation algorithms, our main focus is to improve our understanding of the stronger configuration LP relaxation. In this direction, we prove that the integrality gap of the configuration LP is strictly better than $\frac{3}{4}$, and provide corresponding polynomial time roundings, in the following restrictions of the problem: (i) the Restricted Budgeted Allocation problem, in which all the players have the same budget and every item has the same value for any player it can be sold to, and (ii) the graph MBA problem, in which an item can be assigned to at most 2 players. Finally, we improve the best known upper bound on the integrality gap for the general case from $\frac{5}{6}$ to $2\sqrt{2}-2\approx 0.828$ and also prove hardness of approximation results for both cases.Comment: 29 pages, 4 figures. To appear in the 17th Conference on Integer Programming and Combinatorial Optimization (IPCO), 201

Applications of Strong Convex Relaxations to Allocation Problems

Approximation algorithms are a commonly used tool for designing efficient algorithmic solutions for intractable problems, at the expense of the quality of the output solution. A prominent technique for designing such algorithms is the use of Linear Programming (LP) relaxations. An optimal solution to such a relaxation provides a bound on the objective value of the optimal integral solution, to which we compare the integral solution we return. In this context, when studying a specific problem, two natural questions often arise: What is a strong LP relaxation for this problem, and how can we exploit it? Over the course of the past few decades, a significant amount of effort has been expended by the research community in order to answer these questions for a variety of interesting intractable problems. Although there exist multiple problems for which we have designed LP relaxations that achieve best-possible guarantees, there still exist numerous problems for which we either have no strong LP relaxations, or do not know how to use them. The main focus of this thesis is extending our understanding of such strong relaxations. We focus on designing good approximation algorithms for certain allocation problems, by employing a class of strong LP relaxations, called configuration-LPs. For many such allocation problems, the best-known results are derived by using simple and natural LP relaxations, whereas configuration-LPs have been used successfully on several occasions in order to break pre-existing barriers set by weaker relaxations. However, our understanding of configuration-LPs is far from complete for many problems. Therefore, understanding and using these relaxations to the farthest extent possible is a quite intriguing question. Answering this question could result in improved approximation algorithms for a wide variety of allocation problems. The first problem we address in this thesis is the restricted max-min fair allocation problem. Prior to our work, the best known result provided an $\Omega(1)$-approximation that ran in polynomial time. Also, it was known how to estimate the value of an optimal solution to the problem within a factor of $1/(4+c)$, for any $c>0$, by solving the corresponding configuration-LP. Our first contribution in this thesis is the design of a $1/13$-approximation algorithm for the problem, using the configuration-LP. Specifically, although our algorithm is fully combinatorial, it consists of a local-search procedure that is guaranteed to succeed only when the configuration-LP is feasible. In order to establish the correctness and running time of the algorithm, it is crucial to use the configuration-LP in our analysis. The second problem we study is the scheduling of jobs on unrelated machines in order to minimize the sum of weighted completion times. For this problem, the best known approximation algorithm achieves a ratio of $3/2-r$, for some small $r>0$. Our second contribution in this thesis is the improvement of this ratio to $(1+\sqrt{2})/2+c$, for any $c>0$, for the special case of the problem where the jobs have uniform Smith ratios. To achieve this ratio, we design a randomized rounding algorithm that rounds solutions to the corresponding configuration-LP. Through a careful examination of the distribution this randomized algorithm outputs, we identify the one that maximizes the approximation ratio, and we then upper bound the ratio this worst-case distribution exhibits by $(1+\sqrt{2})/2+c$

DNA-Based Approaches for Traceability and Authentication of Olive Oil

Authentication and traceability of extra virgin olive oil is a challenging research task due to the complexity of fraudulent practices. Various chemical and biochemical techniques have been developed for determining the authenticity of olive oil and in recent years non-conventional methods based on DNA analysis have gained attention, due to high specificity, sensitivity and reliability. DNA analyses have very high discriminating power because ultimately the unique identity of a variety or species is to a great extent genetically dependent. Polymorphisms are genetic variations which refer to the variation in populations or species. Molecular markers provide information on genetic variations and are valuable tools to determine olive oil authenticity. Recently several DNA-based methods have been developed to authenticate olive oil, since analysis of the residual oil DNA with the use of molecular markers can lead to the identification of the variety or the plant species from which it was extracted. The aim of this chapter is to provide an overview of the current trends and critical issues on DNA-targeted approaches used for traceability and authenticity of olive oil. This is considered a rapidly expanding field with significant challenges and prospects which shall be discussed thoroughly

Osteolytic bone destruction resulting from relapse of a testicular tumour 23 years after inguinal orchiectomy and adjuvant chemotherapy: a case report

<p>Abstract</p> <p>Introduction</p> <p>Late relapse of a testicular germ cell tumour is an uncommon occurrence. We report a case of osteolytic bone metastasis appearing 23 years after the initial treatment of a metastatic testicular mixed tumour (choriocarcinoma and embryonal carcinoma). This is one of the longest periods of recurrence reported for testicular germ cell tumours.</p> <p>Case presentation</p> <p>A 52-year-old Caucasian man who underwent a right inguinal orchiectomy due to testicular tumour in 1984 presented to our outpatient clinic in a generally bad condition of health and with severe pain of his right hip joint and os ischii caused by osteolytic metastasis.</p> <p>Conclusions</p> <p>This case emphasizes the need for a life-long follow-up of patients with primary metastatic testicular cancer.</p

Perforation of the Urinary Bladder Caused by Transurethral Insertion of a Pencil for the Purpose of Masturbation in a 29-Year-Old Female

The urethra is a usual site of introduction of foreign bodies for autoerotic stimulation. We present an unusual case of bladder perforation caused by foreign body that was self-inserted in the urethra and consequently slipped inside the bladder in a 29-year-old female patient with psychiatric disease. The patient was referred to our department for macroscopic hematuria and abdominal pain. Imaging studies revealed the presence of a foreign body in the pelvic area which had perforated the left lateral wall of the bladder. The foreign body was removed via open cystotomy. In psychiatric patients hematuria and pelvic pain may result from insertion of a foreign body in the bladder usually during masturbation

Clinical Study Ureteroscopic Laser Treatment of Upper Urinary Tract Urothelial Cell Carcinomas: Can a Tumour Free Status Be Achieved?

Introduction. In cases of anatomic or functional single kidney with urothelial tumours of the upper urinary tract, the endoscopic laser ablation has proven efficacious. Based on the knowledge that low-grade, low-stage upper tract transitional cell carcinomas rarely progress to invasive lesions, indications for endoscopic laser ablation have expanded to include patients with bilateral functioning kidneys and low-grade tumours. The question that remains to be answered is whether endoscopic laser ablation has the ability to completely eradicate upper urinary tract tumours. Methods. We performed in 25 patients in a period of 11 years 288 ureteroscopies and, if needed, laser ablation of upper urinary tract tumours in imperative indication. Results. In 32% of the patients the cancer remained even after several laser sessions. 64% of patients were tumour free after one or more laser sessions but remained clear only for the next 3 months. Only 1 patient was tumour free for a period of 68 months after 1 session of laser treatment. The procedure had low complication rates. Conclusion. The laser technology and the introduction of small diameter semirigid and flexible ureteroscopes made ablation of upper urinary tract tumours possible and safe. Nevertheless a complete resection of the carcinomas is rarely possible

Combinatorial Algorithm for Restricted Max-Min Fair Allocation

We study the basic allocation problem of assigning resources to players so as to maximize fairness. This is one of the few natural problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed, a certain configuration-LP can be used to estimate the value of the optimal allocation to within a factor of 4 + ε. In contrast, however, the best known approximation algorithm for the problem has an unspecified large constant guarantee. In this paper we significantly narrow this gap by giving a 13-approximation algorithm for the problem. Our approach develops a local search technique introduced by Haxell [Hax95] for hypergraph matchings, and later used in this context by Asadpour, Feige, and Saberi [AFS12]. For our local search procedure to terminate in polynomial time, we introduce several new ideas such as lazy updates and greedy players. Besides the improved approximation guarantee, the highlight of our approach is that it is purely combinatorial and uses the configuration-LP only in the analysis

Synergistic exploitation of geoinformation methods for post-earthquake 3D mapping of Vrisa traditional settlement, Lesvos Island, Greece

The aim of this paper is to present the methodology followed and the results obtained by the synergistic exploitation of geo-information methods towards 3D mapping of the impact of the catastrophic earthquake of June 12th 2017 on the traditional settlement of Vrisa on the island of Lesvos, Greece. A campaign took place for collecting: a) more than 150 ground control points using an RTK system, b) more than 20.000 high-resolution terrestrial and aerial images using cameras and Unmanned Aircraft Systems and c) 140 point clouds by a 3D Terrestrial Laser Scanner. The Structure from Motion method has been applied on the high-resolution terrestrial and aerial photographs, for producing accurate and very detailed 3D models of the damaged buildings of the Vrisa settlement. Additionally, two Orthophoto maps and Digital Surface Models have been created, with a spatial resolution of 5cm and 3cm, respectively. The first orthophoto map has been created just one day after the earthquake, while the second one, a month later. In parallel, 3D laser scanning data have been exploited in order to validate the accuracy of the 3D models and the RTK measurements used for the geo-registration of all the above-mentioned datasets. The significant advantages of the proposed methodology are: a) the coverage of large scale areas; b) the production of 3D models having very high spatial resolution and c) the support of post-earthquake management and reconstruction processes of the Vrisa village, since such 3D information can serve all stakeholders, be it national and/or local organizations