Approximating random quantum optimization problems

Approximating Incremental Combinatorial Optimization Problems

We consider incremental combinatorial optimization problems, in which a solution is constructed incrementally over time, and the goal is to optimize not the value of the final solution but the average value over all timesteps. We consider a natural algorithm of moving towards a global optimum solution as quickly as possible. We show that this algorithm provides an approximation guarantee of (9 ...

Approximating Concavely Parameterized Optimization Problems

We consider an abstract class of optimization problems that are parameterized concavely in a single parameter, and show that the solution path along the parameter can always be approximated with accuracy ε > 0 by a set of sizeO(1/ √ ε). A lower bound of size Ω(1/ √ ε) shows that the upper bound is tight up to a constant factor. We also devise an algorithm that calls a step-size oracle and compu...

Approximating layout problems on random graphs

We show that, with overwhelming probability, several well known layout problems are approximable within a constant for random graphs drawn from the G(n, pn) model where C/n ≤ pn ≤ 1 for all n big enough and for some properly characterized parameter C > 1. In fact, our results establish that, with overwhelming probability, the cost of any arbitrary layout of such a random graph is within a const...

Approximating Layout Problems on Random Geometric Graphs

In this paper, we study the approximability of several layout problems on a family of random geometric graphs. Vertices of random geometric graphs are randomly distributed on the unit square and are connected by edges whenever they are closer than some given parameter. The layout problems that we consider are: Bandwidth, Minimum Linear Arrangement, Minimum Cut Width, Minimum Sum Cut, Vertex Sep...

Approximating Multi-Objective Time-Dependent Optimization Problems