Our paper on Market pricing for matroid rank valuations has been recently accepted for publication in SIAM Journal on Discrete Mathematics. In the paper, we study the problem of maximizing social welfare in combinatorial markets through pricing schemes. We consider the existence of prices that are capable to achieve optimal social welfare without a central…
How does a greedy solution perform in terms of approximation? In our recent paper Approximation by lexicographically maximal solutions in matching and matroid intersection problems, we study how good a lexicographically maximal solution is in the weighted matching and matroid intersection problems. A solution is lexicographically maximal if it takes as many heaviest elements as…
Our manuscript on dynamic pricing schemes in bi-demand markets is now available on arXiv, see http://arxiv.org/abs/2107.05131. In contrast to static models, the dynamic setting allows to update the prices between buyer-arrivals, therefore it is capable to achieve maximum social welfare without a central coordinator. Continuing the work of Cohen-Addad et al. and Berger et al.,…
Our paper titled List colouring of two matroids through reduction to partition matroids has been accepted for publication in SIAM Journal on Discrete Mathematics! The paper focuses on the question whether the list coloring number of the intersection of two matroids can be bounded by a constant times the coloring number. We consider matroid classes…
Anyone who has worked with matroids has come away with the conviction that matroids are one of the richest and most useful ideas of our day. – Gian Carlo Rota