Search results for "Binary search algorithm"
showing 4 items of 4 documents
Fast Algorithms for Pseudoarboricity
2015
The densest subgraph problem, which asks for a subgraph with the maximum edges-to-vertices ratio d∗, is solvable in polynomial time. We discuss algorithms for this problem and the computation of a graph orientation with the lowest maximum indegree, which is equal to ⌈d∗⌉. This value also equals the pseudoarboricity of the graph. We show that it can be computed in O(|E| √ log log d∗) time, and that better estimates can be given for graph classes where d∗ satisfies certain asymptotic bounds. These runtimes are achieved by accelerating a binary search with an approximation scheme, and a runtime analysis of Dinitz’s algorithm on flow networks where all arcs, except the source and sink arcs, hav…
Optimal standalone data center renewable power supply using an offline optimization approach
2022
Abstract Because of the increasing energy consumption of data centers and their C O 2 emissions, the ANR DATAZERO2 project aims to design autonomous data centers running solely on local renewable energy coupled with storage devices to overcome the intermittency issue. In order to optimize the use of renewable energy and storage devices, a MILP solver is usually in charge of assigning the power to be supplied to the data center. However, in order to reduce the computation time and make the approach scalable, it would be more appropriate to use a polynomial time algorithm. This paper aims at showing and proving that it is possible to provide an optimal power profile via a deterministic algori…
A new compact formulation for the discrete p-dispersion problem
2017
Abstract This paper addresses the discrete p -dispersion problem (PDP) which is about selecting p facilities from a given set of candidates in such a way that the minimum distance between selected facilities is maximized. We propose a new compact formulation for this problem. In addition, we discuss two simple enhancements of the new formulation: Simple bounds on the optimal distance can be exploited to reduce the size and to increase the tightness of the model at a relatively low cost of additional computation time. Moreover, the new formulation can be further strengthened by adding valid inequalities. We present a computational study carried out over a set of large-scale test instances i…
Combined IT and power supply infrastructure sizing for standalone green data centers
2021
International audience; In this work, we propose a two-step methodology for designing and sizing a data center solely powered by local renewable energy. The first step consists in determining the necessary IT equipment for processing a given IT workload composed of batch and service tasks. We propose an adapted binary search algorithm and prove its optimality to find the minimum number of servers to handle the IT workload. When the IT sizing is computed, the second step consists in defining the supplying electrical infrastructure using wind turbines and photovoltaic panels as primary sources. Batteries and a hydrogen system are added as secondary sources for short- and long-term energy stor…