Censor-Hillel et al. [PODC’15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in the past few years. This paper develops further algebraic techniques for designing algorithms in this model. We present deterministic and randomized algorit...

A path (resp. cycle) decomposition of a graph G is a set of edge-disjoint paths (resp. cycles) of G that covers the edge set of G. Gallai (1966) conjectured that every graph on n vertices admits a path decomposition of size at most ⌊(n+ 1)/2⌋, and Hajós (1968) conjectured that every Eulerian graph on n vertices admits a cycle decomposition of size at most ⌊(n−1)/2⌋. Gallai’s Conjecture was veri...

The notion of limits of dense graphs was invented, among other reasons, to attack problems in extremal graph theory. It is straightforward to define limits of order types in analogy with limits of graphs, and this paper examines how to adapt to this setting two approaches developed to study limits of dense graphs. We first consider flag algebras, which were used to open various questions on gra...