We show that the multi-commodity max-flow/min-cut gap for series-parallel graphs can be as bad as 2, matching a recent upper bound [8] for this class, and resolving one side of a ...
We show that any face hitting set of size n of a connected planar graph with a minimum degree of at least 3 is contained in a connected subgraph of size 5n − 6. Furthermore we s...
A transposition is an operation that exchanges two adjacent substrings. When it is restricted so that one of the substrings is a prefix, it is called a prefix transposition. The p...
Suppose we have n algorithms, quantum or classical, each computing some bit-value with bounded error probability. We describe a quantum algorithm that uses O( √ n) repetitions of...
We show how to implement an arbitrary two-qubit unitary operation using any of several quantum gate libraries with small a priori upper bounds on gate counts. In analogy to librar...
Vivek V. Shende, Igor L. Markov, Stephen S. Bulloc...