Multitasking Capacity: Hardness Results and Improved Constructions

We consider the problem of determining the maximal $\alpha \in (0,1]$ such that every matching $M$ of size $k$ (or at most $k$) in a bipartite graph $G$ contains an induced matching of size at least $\alpha |M|$. This measure was recently introduced in Alon et al. (NIPS 2018) and is motivated by connectionist models of cognition as well...More