@article{CsehFaenzaKavithaetal.2022, author = {Cseh, Agnes and Faenza, Yuri and Kavitha, Telikepalli and Powers, Vladlena}, title = {Understanding popular matchings via stable matchings}, series = {SIAM journal on discrete mathematics}, volume = {36}, journal = {SIAM journal on discrete mathematics}, number = {1}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {0895-4801}, doi = {10.1137/19M124770X}, pages = {188 -- 213}, year = {2022}, abstract = {An instance of the marriage problem is given by a graph G = (A boolean OR B, E), together with, for each vertex of G, a strict preference order over its neighbors. A matching M of G is popular in the marriage instance if M does not lose a head-to-head election against any matching where vertices are voters. Every stable matching is a min-size popular matching; another subclass of popular matchings that always exists and can be easily computed is the set of dominant matchings. A popular matching M is dominant if M wins the head-to-head election against any larger matching. Thus, every dominant matching is a max-size popular matching, and it is known that the set of dominant matchings is the linear image of the set of stable matchings in an auxiliary graph. Results from the literature seem to suggest that stable and dominant matchings behave, from a complexity theory point of view, in a very similar manner within the class of popular matchings. The goal of this paper is to show that there are instead differences in the tractability of stable and dominant matchings and to investigate further their importance for popular matchings. First, we show that it is easy to check if all popular matchings are also stable; however, it is co-NP hard to check if all popular matchings are also dominant. Second, we show how some new and recent hardness results on popular matching problems can be deduced from the NP-hardness of certain problems on stable matchings, also studied in this paper, thus showing that stable matchings can be employed to show not only positive results on popular matchings (as is known) but also most negative ones. Problems for which we show new hardness results include finding a min-size (resp., max-size) popular matching that is not stable (resp., dominant). A known result for which we give a new and simple proof is the NP-hardness of finding a popular matching when G is nonbipartite.}, language = {en} } @article{SysłoKwiatkowska2015, author = {Sysło, Maciej M. and Kwiatkowska, Anna Beata}, title = {Think logarithmically!}, series = {KEYCIT 2014 - Key Competencies in Informatics and ICT}, journal = {KEYCIT 2014 - Key Competencies in Informatics and ICT}, number = {7}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {1868-0844}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-82923}, pages = {371 -- 380}, year = {2015}, abstract = {We discuss here a number of algorithmic topics which we use in our teaching and in learning of mathematics and informatics to illustrate and document the power of logarithm in designing very efficient algorithms and computations - logarithmic thinking is one of the most important key competencies for solving real world practical problems. We demonstrate also how to introduce logarithm independently of mathematical formalism using a conceptual model for reducing a problem size by at least half. It is quite surprising that the idea, which leads to logarithm, is present in Euclid's algorithm described almost 2000 years before John Napier invented logarithm.}, language = {en} } @article{CsehHeeger2020, author = {Cseh, Agnes and Heeger, Klaus}, title = {The stable marriage problem with ties and restricted edges}, series = {Discrete optimization}, volume = {36}, journal = {Discrete optimization}, publisher = {Elsevier}, address = {Amsterdam}, issn = {1572-5286}, doi = {10.1016/j.disopt.2020.100571}, pages = {11}, year = {2020}, abstract = {In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class. A matching is called stable if it is not blocked by any pair of agents, who mutually prefer each other to their respective partner. Ties in the preferences allow for three different definitions for a stable matching: weak, strong and super-stability. Besides this, acceptable pairs in the instance can be restricted in their ability of blocking a matching or being part of it, which again generates three categories of restrictions on acceptable pairs. Forced pairs must be in a stable matching, forbidden pairs must not appear in it, and lastly, free pairs cannot block any matching. Our computational complexity study targets the existence of a stable solution for each of the three stability definitions, in the presence of each of the three types of restricted pairs. We solve all cases that were still open. As a byproduct, we also derive that the maximum size weakly stable matching problem is hard even in very dense graphs, which may be of independent interest.}, language = {en} } @article{ToppingAlroeFarrelletal.2015, author = {Topping, Christopher J. and Alroe, Hugo Fjelsted and Farrell, Katharine N. and Grimm, Volker}, title = {Per Aspera ad Astra: Through Complex Population Modeling to Predictive Theory}, series = {The American naturalist : a bi-monthly journal devoted to the advancement and correlation of the biological sciences}, volume = {186}, journal = {The American naturalist : a bi-monthly journal devoted to the advancement and correlation of the biological sciences}, number = {5}, publisher = {Univ. of Chicago Press}, address = {Chicago}, issn = {0003-0147}, doi = {10.1086/683181}, pages = {669 -- 674}, year = {2015}, abstract = {Population models in ecology are often not good at predictions, even if they are complex and seem to be realistic enough. The reason for this might be that Occam's razor, which is key for minimal models exploring ideas and concepts, has been too uncritically adopted for more realistic models of systems. This can tic models too closely to certain situations, thereby preventing them from predicting the response to new conditions. We therefore advocate a new kind of parsimony to improve the application of Occam's razor. This new parsimony balances two contrasting strategies for avoiding errors in modeling: avoiding inclusion of nonessential factors (false inclusions) and avoiding exclusion of sometimes-important factors (false exclusions). It involves a synthesis of traditional modeling and analysis, used to describe the essentials of mechanistic relationships, with elements that arc included in a model because they have been reported to be or can arguably be assumed to be important under certain conditions. The resulting models should be able to reflect how the internal organization of populations change and thereby generate representations of the novel behavior necessary for complex predictions, including regime shifts.}, language = {en} }