Computational complexity | EPFL Graph Search

In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory. Both areas are highly related, as the complexity of an algorithm is always an upper bound on the complexity of the problem solved by this algorithm. Moreover, for designing efficient algorithms, it is often fundamental to compare the complexity of a specific algorithm to the complexity of the problem to be solved. Also, in most cases, the only thing that is known about the complexity of a problem is that it is lower than the comple

Decentralized in-order execution of a sequential task-based code for shared-memory architectures

Charly Nicolas Lucien Castes

The hardware complexity of modern machines makes the design of adequate programming models crucial for jointly ensuring performance, portability, and productivity in high-performance computing (HPC). Sequential task-based programming models paired with advanced runtime systems allow the programmer to write a sequential algorithm independently of the hardware architecture in a productive and portable manner, and let a third party software layer -the runtime system- deal with the burden of scheduling a correct, parallel execution of that algorithm to ensure performance. Many HPC algorithms have successfully been implemented following this paradigm, as a testimony of its effectiveness. Developing algorithms that specifically require fine-grained tasks along this model is still considered prohibitive, however, due to per-task management overhead [1], forcing the programmer to resort to a less abstract, and hence more complex "task+X" model. We thus investigate the possibility to offer a tailored execution model, trading dynamic mapping for efficiency by using a decentralized, conservative in-order execution of the task flow, while preserving the benefits of relying on the sequential taskbased programming model. We propose a formal specification of the execution model as well as a prototype implementation, which we assess on a shared-memory multicore architecture with several synthetic workloads. The results show that under the condition of a proper task mapping supplied by the programmer, the pressure on the runtime system is significantly reduced and the execution of fine-grained task flows is much more efficient.

IEEE COMPUTER SOC2022

Robust Portfolio Optimization

Zheng Wei Yap

Since the 2008 Global Financial Crisis, the financial market has become more unpredictable than ever before, and it seems set to remain so in the forseeable future. This means an investor faces unprecedented risks, hence the increasing need for robust portfolio optimization to protect them against uncertainty, which is potentially devastating if unattended yet ignored in the classical Markowitz model, whose another deficiency is the absence of higher moments in its assumption of the distribution of asset returns. We establish an equivalence between the Markowitz model and the portfolio return value-at-risk optimization problem under multivariate normality of asset returns, so that we can add these excluded features into the former implicitly by incorporating them into the latter. We also provide a probabilistic smoothing spline approximation method and a deterministic model within the location-scale framework under elliptical distribution of the asset returns to solve the robust portfolio return value-at-risk optimization problem. In particular for the deterministic model, we introduce a novel eigendecomposition uncertainty set which lives in the positive definite space for the scale matrix without compromising on the computational complexity and conservativeness of the optimization problem, invent a method to determine the size of the involved uncertainty sets, test it out on real data, and explore its diversification properties. Although the value-at-risk has been the standard risk measure adopted by the banking and insurance industry since the early nineties, it has since attracted many criticisms, in particular from McNeil et al. (2005) and the Basel Committee on Banking Supervision in 2012, also known as Basel 3.5. Basel 4 even suggests a move away from the what" value-at-risk to the what-if" conditional value-at-risk' measure. We shall see that the former may be replaced with the latter or even other risk measures in our formulations easily.

EPFL2017

The gene family-free median of three

Metin Balaban

Background: The gene family-free framework for comparative genomics aims at providing methods for gene order analysis that do not require prior gene family assignment, but work directly on a sequence similarity graph. We study two problems related to the breakpoint median of three genomes, which asks for the construction of a fourth genome that minimizes the sum of breakpoint distances to the input genomes. Methods: We present a model for constructing a median of three genomes in this family-free setting, based on maximizing an objective function that generalizes the classical breakpoint distance by integrating sequence similarity in the score of a gene adjacency. We study its computational complexity and we describe an integer linear program (ILP) for its exact solution. We further discuss a related problem called family-free adjacencies for k genomes for the special case of k

2017

Robust Portfolio Optimization

Zheng Wei Yap

EPFL2017