Abstract The problem of model counting, also known as $$\#\textsf{SAT}$$ # SAT , is to compute the number models or satisfying assignments a given Boolean formula F . Model counting fundamental in computer science with wide range applications. In recent years, there has...

Following previous theoretical work by Srinivasan (FOCS 2001) and the first author (STACS 2006) and a first experimental evaluation on random instances (ALENEX 2009), we investigate how the recently developed different approaches to generate randomized roundings satisfying disjoint cardinality constraints behave when used in two classical algorithmic problems, namely low-congestion routing in n...

In out last lecture, we discussed the LP Rounding technique for producing approximation algorithms. The idea behind LP Rounding is to write the problem as an integer linear program, relax its integrality restraints to efficiently solve the general linear program, and then move the LP solution to a nearby integral point in the feasible solution space. The difficulty of this process lies in the r...

The tensor-train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT particularly useful when representing approximations to the solutions of certain types parametrized partial differential equations. For many these problems, computing solution explicitly would require an infeasible amount memory and computational time. While makes problems tractable, iterat...

We introduce a new technique called oblivious rounding | a variant of randomized rounding that avoids the bottleneck of rst solving the linear program. Avoiding this bottleneck yields more eecient algorithms and brings probabilistic methods to bear on a new class of problems. We give oblivious rounding algorithms that approximately solve general packing and covering problems, including a parall...

Rounding of the so-called infinite precision coefficients to their nearest finite wordlength representation is often used for reasons of simplicity. This rounding, however, is typically far from optimal. A significantly better rounding method that uses a technique called telescoping is presented in this paper. Its practical effectiveness in the design of suboptimal finite wordlength filters is ...