Many discrete optimization problems are naturally modeled as an integer (linear) programming (ILP) problem. An ILP problem is of the form max cx Ax ≤ b x is an integer vector. (1) It is easy to show that ILP is NP-hard via a reduction from say SAT. The decision version of ILP is the following: Given rational matrix A and rational vector b, does Ax ≤ b have an integral solution x? Theorem 1 Deci...

Encryption in which “your name is your public key” is called Identity-Based Encryption (IBE). Shamir’s original motivation for identity-based encryption was to simplify the management of public keys. Frequently, this process can be unwieldy because of the following problem: if Bob obtains Alice’s public key over the network, how does Bob know that the key really belongs to Alice, and not to a m...

Figure 1: This is the example, illustrating the proof above. The black matching is M and the orange matching is M ′. The lists beside m,w shows their preference list. We know that m prefers his match in the black matching, w, to his match in the orange matching, w′. For purposes of contradiction, we assumed that w prefers m to m′. As you can see, this implies that the pair (m,w) is an instabili...

We report on our experience with an approach to debriefing that emphasizes disclosing instructors' judgments and eliciting trainees' assumptions about the situation and their reasons for acting as they did. To highlight the importance of instructors disclosing their judgment skillfully, we call the approach "debriefing with good judgment." The approach draws on theory and empirical findings fro...