Any-Order Online Interval Selection

We consider the problem of online interval scheduling on a single machine, where intervals arrive online in an order chosen by an adversary, and the algorithm must output a set of non-conflicting intervals. Traditionally in scheduling theory, it is assumed that intervals arrive in order of increasing start times. We drop that assumption and allow for intervals to arrive in any possible order. We call this variant any-order interval selection (AOIS). We assume that some online acceptances can be revoked, but a feasible solution must always be maintained. For unweighted intervals and deterministic algorithms, this problem is unbounded. Under the assumption that there are at most $k$ different interval lengths, we give a simple algorithm that achieves a competitive ratio of $2k$ and show that it is optimal amongst deterministic algorithms, and a restricted class of randomized algorithms we call memoryless, contributing to an open question by Adler and Azar 2003; namely whether a randomized algorithm without access to history can achieve a constant competitive ratio. We connect our model to the problem of call control on the line, and show how the algorithms of Garay et al. 1997 can be applied to our setting, resulting in an optimal algorithm for the case of proportional weights. We also discuss the case of intervals with arbitrary weights, and show how to convert the single-length algorithm of Fung et al. 2014 into a classify and randomly select algorithm that achieves a competitive ratio of 2k. Finally, we consider the case of intervals arriving in a random order, and show that for single-lengthed instances, a one-directional algorithm (i.e. replacing intervals in one direction), is the only deterministic memoryless algorithm that can possibly benefit from random arrivals. Finally, we briefly discuss the case of intervals with arbitrary weights.Comment: 19 pages, 11 figure

Greedy Bipartite Matching in Random Type Poisson Arrival Model

We introduce a new random input model for bipartite matching which we call the Random Type Poisson Arrival Model. Just like in the known i.i.d. model (introduced by Feldman et al. [Feldman et al., 2009]), online nodes have types in our model. In contrast to the adversarial types studied in the known i.i.d. model, following the random graphs studied in Mastin and Jaillet [A. Mastin, 2013], in our model each type graph is generated randomly by including each offline node in the neighborhood of an online node with probability c/n independently. In our model, nodes of the same type appear consecutively in the input and the number of times each type node appears is distributed according to the Poisson distribution with parameter 1. We analyze the performance of the simple greedy algorithm under this input model. The performance is controlled by the parameter c and we are able to exactly characterize the competitive ratio for the regimes c = o(1) and c = omega(1). We also provide a precise bound on the expected size of the matching in the remaining regime of constant c. We compare our results to the previous work of Mastin and Jaillet who analyzed the simple greedy algorithm in the G_{n,n,p} model where each online node type occurs exactly once. We essentially show that the approach of Mastin and Jaillet can be extended to work for the Random Type Poisson Arrival Model, although several nontrivial technical challenges need to be overcome. Intuitively, one can view the Random Type Poisson Arrival Model as the G_{n,n,p} model with less randomness; that is, instead of each online node having a new type, each online node has a chance of repeating the previous type

NON-FARADAIC ELECTROCHEMICAL MODIFICATION OF CATALYTIC ACTIVITY OF AG. THE CASEOF CO OXIDATION AND C2H4 EPOXIDATION

ΒΡΕΘΗΚΕ ΟΤΙ Η ΕΝΕΡΓΟΤΗΤΑ ΤΟΥ ΠΟΛΥΚΡΥΣΤΑΛΛΙΚΟΥ AG ΓΙΑ ΤΗΝ ΟΞΕΙΔΩΣΗ ΤΟΥ CO ΚΑΙ ΤΗΝ ΕΠΟΞΕΙΔΩΣΗ ΤΟΥ C2H4, ΕΙΝΑΙ ΔΥΝΑΤΟΝ ΝΑ ΕΠΗΡΕΑΣΘΕΙ ΜΕ ΗΛΕΚΤΡΟΧΗΜΙΚΗ ΑΝΤΛΗΣΗ ΙΟΝΤΩΝ ΠΡΟΣ Η ΑΠΟ ΤΗΝ ΚΑΤΑΛΥΤΙΚΗ ΕΠΙΦΑΝΕΙΑ. ΟΙ ΑΝΤΙΔΡΑΣΕΙΣ ΜΕΛΕΤΗΘΗΚΑΝ ΣΕ ΣΤΟΙΧΕΙΟ ΣΤΑΘΕΡΟΠΟΙΗΜΕΝΗΣ ΖΙΡΚΟΝΙΑΣ (ΑΓΩΓΟΣ Ο2-) ΚΑΙ Β"-AL2O3 (ΑΓΩΓΟΣ NA+). ΚΑΤΑ ΤΗΝ ΟΞΕΙΔΩΣΗ ΤΟΥ C2H4, ΜΕ ΑΝΤΛΗΣΗ ΙΟΝΤΩΝ NA+ ΠΡΟΣ ΤΗΝ ΚΑΤΑΛΥΤΙΚΗ ΕΠΙΦΑΝΕΙΑ ΚΑΙ ΤΑΥΤΟΧΡΟΝΗ ΠΡΟΣΘΗΚΗ ΣΤΗΝ ΤΡΟΦΟΔΟΣΙΑ ΧΛΩΡΙΩΜΕΝΟΥ ΥΔΡΟΓΟΝΑΝΘΡΑΚΑ, ΜΕΤΡΗΘΗΚΑΝ ΕΚΛΕΚΤΙΚΟΤΗΤΕΣ ΩΣ ΠΡΟΣ C2H4O ΜΕΧΡΙ ΚΑΙ 88%. ΤΑ ΠΑΡΑΠΑΝΩ ΑΠΟΔΙΔΟΝΤΑΙ ΣΕ ΑΛΛΑΓΗ ΤΟΥ ΕΡΓΟΥ ΕΞΟΔΟΥ ΤΟΥ AG.IT WAS FOUND THAT THE CATALYTIC ACTIVITY OF POLYCRYSTALLINE AG, FOR CO OXIDATION AND C2H4 EPOXIDATION, CAN BE AFFECTED SIGNIFICANTLY BY ELECTROCHEMICAL ION PUMPING TO OR FROM THE CATALYST SURFACE. THE REACTIONS WERE STUDIED IN AN YTTRIA-STABILIZED ZIRCONIA (O2-CONDUCTOR) B"-AL2O3 CELL (NA+ CONDUCTOR). FOR C2H4 EPOXIDATION, BY NA+ PUMPING TO THE SURFACE AND IN THE PRESENCE OF CHLORINATED HYDROCARBON IN THE GAS PHASE SELECTIVITY VALUES OF C2H4O AS HIGH AS 88% CAN BE OBTAINED. THE OBSERVED PHENOMENA ARE INTERPRETED WITHIN THE FRAMEWORK OF PREVIOUS NEMCA STUDIES AND REGARDING THE CHANGES OF AG WORK FUNCTION