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In this work we improve the approximation factors to .845$ and .709$, respectively.
We also consider an online version of the bipartite case, where one side of the partition arrives node by node, and each time a node $b$ arrives we have to decide which edges incident to $b$ we want to probe, and in which order.
We know whether an edge exists or not only after probing it.
On this random graph we are executing a process, which one-by-one probes the edges and gradually constructs a matching.
In this paper we consider the Stochastic Matching problem, which is motivated by applications in kidney exchange and online dating.
We are given an undirected graph in which every edge is assigned a probability of existence and a positive profit, and each node is assigned a positive integer called timeout.
A similar challenge is that these products aren’t “social” in the same way that Skype or Facebook might be.
Although the stigma is quickly passing, it’s not like consumers want to sign up for a dating site and then invite their friends family to join them on the site.
As you might imagine, that creates the wrong incentives.
A product focused on casual dating, like Tinder, might escape this dilemma, but dating products generally have built-in churn that’s unavoidable.
Obviously, anyone starting a new company in dating should try to understand investor biases in this sector.