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We introduce the notion of counting oracles for various path problems in graphs. We present an oracle for counting the number of shortest paths between a pair of vertices in any planar graph which takes

We initiate the study of multi-layered cake cutting with goal of fairness among a set of agents. We impose a restriction that each agent may only receive a single resource at each time interval. This

The maximin share guarantee (MMS) is a common fairness notion in the field of fair division of indivisible goods. Since MMS is not guaranteed to exist in general, many approximation schemes have been studied. One

Fair Item Allocation Have you ever had to divide candy among your picky friends? Perhaps you want to divide an estate among possible heirs. These problems fall into the category of item allocation. Our goal