Pareto optimal matchings in many-to-many markets with ties

We consider Pareto optimal matchings (POMs) in a many-to-many market of applicants and courses where applicants have preferences, which may include ties, over individual courses and lexicographic preferences over sets of courses. Since this is the most general setting examined so far in the literature, our work unifies and generalizes several known results. Specifically, we characterize POMs and introduce the Generalized Serial Dictatorship Mechanism with Ties (GSDT) that effectively handles ties via properties of network flows. We show that GSDT can generate all POMs using different priority orderings over the applicants, but it satisfies truthfulness only for certain such orderings. This shortcoming is not specific to our mechanism; we show that any mechanism generating all POMs in our setting is prone to strategic manipulation. This is in contrast to the one-to-one case (with or without ties), for which truthful mechanisms generating all POMs do exist

2-μερή και πολύ-μερή ευσταθή ταιριάσματα: δομές, αλγόριθμοι και εφαρμογές

This thesis examines the Stable Matching problem (SM) and some of its most important variants, namely the Stable Admissions (SAX the many-to-many Stable Matching (MM), and the Chain Stable Network problem. In the context of the SM, a time-optimal algorithm is provided that identifies which of the non-stable pairs can be removed from the agents' preference lists without altering the set of solutions. Then, using a directed line-graph to represent the SM, a sparse description of the SM polytope is derived. This description is further reduced to obtain the minimal one by identifying the minimal equation system and the facets of the corresponding polytope. Also, the dimension of the SM polytope is proved to be equal to the number of rotations, while its diameter is also established. Moreover, the alternative rotation-based representation of the SM polytope is also examined. Further, rotations are defined in the SA setting and a time-optimal algorithm for identifying all rotations and all non-stable pairs is proposed. This algorithm is then extended to the MM case under pairwise stability, preferences over individuals, and the max-min criterion. In order to maintain the algorithms optimal complexity, the use of a double-stack is proposed. Next, the corresponding rotation-poset graph is revisited and a time- and space-optimal algorithm for enumerating all solutions to the MM is illustrated. Then, a polynomial algorithm for finding the minimum-weight stable matching is provided, which is shown to be applicable even in the case of more complex preference and stability conditions. In a Constraint Programming (CP) context, it is shown that identifying all stable pairs in the SA and the MM case is equivalent to establishing hyperarc consistency. Furthermore, a predicate which models the MM and its encoding as a Constraint Satisfaction Problem is provided. Also, establishing hyperarc consistency as a preprocessing step in a CP platform is proposed, thus obtaining an efficient programming tool, especially in the case where side-constraints are present. Last, a multi-sided Supply Chain Network (SCN) configuration is examined. Under this reduced setting, it is proved that every such £-sided SCN can be decomposed into k-1 independent SM sub-markets. Moreover, it is shown that the set of chain stable networks forms a distributive lattice. Furthermore, the notion of contract-rotations is defined and a series of specialized algorithms are proposed.Η διατριβή αυτή εξετάζει το πρόβλημα του Ευσταθούς Ταιριάσματος (ET), της Ευσταθούς Εισαγωγής (ΕΕ), του πολλά-προς-πολλά Ευσταθούς Ταιριάσματος (ΊΊΠ) και της Ευσταθούς Εφοδιαστικής Αλυσίδας (ΕΕΑ). Στα πλαίσια του ET, παρέχεται ένας χρονικά βέλτιστος αλγόριθμος που αναγνωρίζει ποια από τα μη ευσταθή ζεύγη μπορούν να αφαιρεθούν από τις λίστες προτίμησης χωρίς να προκαλέσουν αλλαγές στο σύνολο των λύσεων. Επιπλέον, χρησιμοποιώντας ένα κατευθυνόμενο γραμμογράφημα και το μειωμένο γράφημα περιστροφών, δίνεται η ελάχιστη περιγραφή του πολυτόπου του ET. Επιπλέον, η διάσταση του αποδεικνύεται ότι είναι ίση με τον αριθμό των περιστροφών, ενώ υπολογίζεται και η διάμετρος του. Ακόμα, εξετάζεται και η εναλλακτική αναπαράσταση του πολυτόπου αυτού που βασίζεται στις περιστροφές. Επίσης, οι περιστροφές ορίζονται στα πλαίσια του ΕΕ, όπου δίνεται ένας χρονικά βέλτιστος αλγόριθμος για την αναγνώριση όλων των περιστροφών και των μη ευσταθών ζευγών. Ο αλγόριθμος αυτός επεκτείνεται και στην περίπτωση του ΠΠ υπό ζευγωτή ευστάθεια, ατομικές προτιμήσεις και το κριτήριο max-min. Μάλιστα, η χρήση μιας διπλής στοίβας προτείνεται για την διατήρηση της βελτιστότητας του αλγορίθμου αυτού. Στη συνέχεια, επανεξετάζονται οι κανόνες κατασκευής του γραφήματος περιστροφών και παρέχεται ένας χρονικά και χωρικά βέλτιστος αλγόριθμος για την απαρίθμηση όλων των λύσεων. Επιπλέον, παρέχεται ένας πολυωνυμικός αλγόριθμος για την εύρεση της λύσης ελαχίστου βάρους, ο οποίος αποδεικνύεται ότι μπορεί να εφαρμοστεί ακόμα και σε περιπτώσεις με πιο περίπλοκες συνθήκες προτιμήσεων και ευστάθειας. Στα πλαίσια του προγραμματισμού περιορισμών (ΉΕ), αποδεικνύεται ότι η αναγνώριση όλων των ευσταθών ζευγών στην περίπτωση του ΕΕ και του ΠΠ ισοδυναμεί με την επίτευξη συνέπειας υπερακμής. Επίσης, παρουσιάζεται ένας περιορισμός ο οποίος μοντελοποιεί το ΠΠ καθώς και η κωδικοποίηση του ως πρόβλημα ικανοποίησης περιορισμών. Επιπλέον, προτείνεται η χρήση του αλγορίθμου που επιτυγχάνει συνέπεια υπερακμής ως ένα προ-επεξεργαστικό βήμα σε μια πλατφόρμα ΠΕ. Η μέθοδος αυτή καταδεικνύεται ότι είναι ιδιαίτερα αποτελεσματική, ιδίως υπό την παρουσία επιπλέον περιορισμών. Τέλος, μελετάται μια εξειδικευμένη εκδοχή του ΕΕΑ. Αποδεικνύεται ότι μία εφοδιαστική αλυσίδα με k σύνολα μπορεί να διαιρεθεί σε k-1 ανεξάρτητες αγορές ET, ενώ η κλίμακα που δημιουργείται από το σύνολο των λύσεων είναι κατανεμημένη. Επιπλέον, ορίζεται η έννοια της περιστροφής συμβολαίων, και παρέχεται μια σειρά από σχετικούς εξειδικευμένους αλγορίθμους

Noname manuscript No. (will be inserted by the editor) On Quantified Linear Implications

Abstract A Quantified Linear Implication (QLI) is an inclusion query over two polyhedral sets, with a quantifier string that specifies which variables are existentially quantified and which are universally quantified. Equivalently, it can be viewed as a quantified implication of two systems of linear inequalities. In this paper, we provide a 2-person game semantics for the QLI problem, which allows us to explore the computational complexities of several of its classes. More specifically, we prove that the decision problem for QLIs with an arbitrary number of quantifier alternations is PSPACE-hard. Furthermore, we explore the computational complexities of several classes of 0, 1, and 2-quantifier alternation QLIs. We observed that some classes are decidable in polynomial time, some are NP-complete, some are coNP-hard and some are Π P 2-hard. We also establish the hardness of QLIs with 2 or more quantifier alternations with respect to the first quantifier in the quantifier string and the number of quantifier alternations. All the proofs that we provide for polynomially solvable problems are constructive, i.e., polynomial-time decision algorithms are devised that utilize well-known procedures. QLIs can be utilized as powerful modelling tools for real-life applications. Such applications include reactive systems, real-time schedulers, and static program analyzers

AIS-Enabled Weather Routing for Cargo Loss Prevention

The operation of any vessel includes risks, such as mechanical failure, collision, property loss, cargo loss, or damage. For modern container ships, safe navigation is challenging as the rate of innovation regarding design, speed profiles, and carrying capacity has experienced exponential growth over the past few years. Prevention of cargo loss in container ship liners is of high importance for the Maritime industry and the waterborne sector as it can lead to potentially disastrous, harmful, or even life-threatening outcomes for the crew, the shipping company, the marine environment, and aqua-culture. With the installment of onboard decision support system(s) (DSS) that will provide the required operational guidance to the vessel’s master, we aim to prevent and overcome such events. This paper explores cargo losses in container ships by employing a novel weather routing optimization DS framework that aims to identify excessive motions and accelerations caused by bad weather at specific times and locations; it also suggests alternative routes and, thus, ultimately prevents cargo loss and damage

AIS-Enabled Weather Routing for Cargo Loss Prevention

The operation of any vessel includes risks, such as mechanical failure, collision, property loss, cargo loss, or damage. For modern container ships, safe navigation is challenging as the rate of innovation regarding design, speed profiles, and carrying capacity has experienced exponential growth over the past few years. Prevention of cargo loss in container ship liners is of high importance for the Maritime industry and the waterborne sector as it can lead to potentially disastrous, harmful, or even life-threatening outcomes for the crew, the shipping company, the marine environment, and aqua-culture. With the installment of onboard decision support system(s) (DSS) that will provide the required operational guidance to the vessel’s master, we aim to prevent and overcome such events. This paper explores cargo losses in container ships by employing a novel weather routing optimization DS framework that aims to identify excessive motions and accelerations caused by bad weather at specific times and locations; it also suggests alternative routes and, thus, ultimately prevents cargo loss and damage

Cognitive Digital Twins for Resilience in Production: A Conceptual Framework

Digital Twins (DTs) are a core enabler of Industry 4.0 in manufacturing. Cognitive Digital Twins (CDTs), as an evolution, utilize services and tools towards enabling human-like cognitive capabilities in DTs. This paper proposes a conceptual framework for implementing CDTs to support resilience in production, i.e., to enable manufacturing systems to identify and handle anomalies and disruptive events in production processes and to support decisions to alleviate their consequences. Through analyzing five real-life production cases in different industries, similarities and differences in their corresponding needs are identified. Moreover, a connection between resilience and cognition is established. Further, a conceptual architecture is proposed that maps the tools materializing cognition within the DT core together with a cognitive process that enables resilience in production by utilizing CDTs