The Heterogeneous Capacitated k-Center Problem

Chakrabarty, Deeparnab; Krishnaswamy, Ravishankar; Kumar, Amit

doi:10.1007/978-3-319-59250-3_11

Cited by 7 publications

(7 citation statements)

References 40 publications

(80 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A well-known variation is to schedule the jobs in order to maximize the minimum machine load, denoted as Q||C min . The problem has received much attention in previous literature, see [1,2,15]. To our knowledge, there has not been made any advances to propose a fixed-parameter algorithm.…”

Section: High-multiplicity Scheduling On Uniformly Related Machinesmentioning

confidence: 99%

See 1 more Smart Citation

Exponentially faster fixed-parameter algorithms for high-multiplicity scheduling

Fischer¹,

Golak²,

Mnich³

2022

Preprint

View full text Add to dashboard Cite

We consider so-called N -fold integer programs (IPs) of the form max{c T x : Ax = b, ℓ ≤ x ≤ u, x ∈ Z nt }, where A ∈ Z (r+sn)×nt consists of n arbitrary matrices A (i) ∈ Z r×t on a horizontal, and n arbitrary matrices B (j) ∈ Z s×t on a diagonal line. Several recent works design fixed-parameter algorithms for N -fold IPs by taking as parameters the numbers of rows and columns of the A-and B-matrices, together with the largest absolute value ∆ over their entries. These advances provide fast algorithms for several well-studied combinatorial optimization problems on strings, on graphs, and in machine scheduling.In this work, we extend this research by proposing algorithms that additionally harness a partition structure of submatrices A (i) and B (j) , where row indices of non-zero entries do not overlap between any two sets in the partition. Our main result is an algorithm for solving any N -fold IP in time nt log(nt)L(S A ) O(r+s) (p A p B ∆) O(rpApB +spApB ) , where p A and p B are the size of the largest set in such a partition of A (i) and B (j) , respectively, S A is the number of parts in the partition of A = (A (1) , . . . , A (n) ), andWe show that these new structural parameters are naturally small in high-multiplicity scheduling problems, such as makespan minimization on related and unrelated machines, with and without release times, the Santa Claus objective, and the weighted sum of completion times. In essence, we obtain algorithms that are exponentially faster than previous works by Knop et al. (ESA 2017) and Eisenbrand et al./Koutecký et al. (ICALP 2018) in terms of the number of job types. We also improve the complexity of minimum sum coloring on graphs of bounded neighborhood diversity.

show abstract

Section: High-multiplicity Scheduling On Uniformly Related Machinesmentioning

confidence: 99%

“…, n, A ∈ Z (r+sn)×nt and b ∈ Z nt . Further, we call the program a uniform N -fold IP if A (1) = A (2) . .…”

Section: Introductionmentioning

confidence: 99%

Exponentially faster fixed-parameter algorithms for high-multiplicity scheduling

Fischer¹,

Golak²,

Mnich³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Since the approximated algorithms for the k-center problem consider general undirected graphs in [29][30][31], a slight modification of the problem would help in the design of an efficient algorithm for identifying k-vertices, called suppliers, with a minimal cost from the operational graph. For the scheduling problem in the directed Microgrid cost graph G = (V, E, w), we build a new undirected operational cost graph G by introducing a dummy connector d with edges e vd (v, d, w vu ) and e ud (u, d, w uv ), where v and u are already associated by directional edges in G. Throughout Algorithm 2, the construction of graph G leads to the transformation of a bidirectional weighted graph into a selective cost graph without direction.…”

Section: Definition 2 (K-center Problem)mentioning

confidence: 99%

Approximation Algorithm-Based Prosumer Scheduling for Microgrids

Shin

2020

Energies

View full text Add to dashboard Cite

Since the inherent intermittency and uncertainty of renewable energy resources complicates efficient Microgrid operations, a Demand Response (DR) scheme is implemented for customers in the grid to alter their power-usage patterns. However, for a real-time pricing model at the current DR, the automated decision on the energy price is not trustworthy because of artificial interferences to the power generation. As opposed to energy price, an operational cost-based prosumer scheduling approach would be able to protect the integrity of the power grid operations from deceptive market transactions and assist in robust energy management. To investigate the operational challenges associated with the costs and prosumers in the Microgrid, we focus on formulating the problem mathematically and designing approximation algorithms to solve the problem of how to optimally identify suppliers to minimize the total operational costs associated with providing electricity. We prove the hardness of the scheduling as one of the NP-Hard problems and propose polynomial time algorithms for approximating optimal solutions. With a proper resilience level for reliable power services, the scheduling algorithms include ways to construct not only robust supplier networks, but also group energy communities in terms of black start while minimizing the operational costs. A series of theoretical performances and experimental evaluations also demonstrates the practical effectiveness of this scheduling model for the operations.

show abstract

“…5 Aquilaria malaccensis (family Thymelaeaceae) was used traditionally as a tonic during pregnancy and after giving birth, as a carminative and to control heart palpitations. 6 It was also prescribed to alleviate jaundice, ulcer, edema, skin diseases, fever, and body aches. 6,7 In addition, the plant was involved in the treatment of central nervous system diseases such as epilepsy and schizophrenia as well as fumigation therapy for sterilization and personal hygiene.…”

Section: Introductionmentioning

confidence: 99%

Phytochemical Constituents of Aquilaria malaccensis Leaf Extract and Their Anti-Inflammatory Activity against LPS/IFN-γ-Stimulated RAW 264.7 Cell Line

et al. 2022

View full text Add to dashboard Cite

This study aims to identify the major phytochemical constituents in Aquilaria malaccensis (Thymelaeaceae) ethanolic leaf extract (ALEX-M) and elucidate their ability to suppress nitric oxide (NO) production from a murine macrophage-like cell line (RAW 264.7) stimulated by lipopolysaccharide (LPS) and interferon-γ (IFN-γ). Dichloromethane (DCM) and ethyl acetate (EtOAc) fractions of ALEX-M were subjected to column chromatography. Eight known compounds were isolated for the first time from this species. Compounds were identified using spectroscopic techniques (IR, UV, HRESIMS, and 1D and 2D NMR). Anti-inflammatory activity of both extract and isolated compounds were investigated in vitro. The fractions offered the isolation of epifriedelanol ( 1 ), 5-hydroxy-7,4′-dimethoxyflavone ( 2 ), luteolin-7,3′,4′-trimethyl ether ( 3 ), luteolin-7,4′-dimethyl ether ( 4 ), acacetin ( 5 ), aquilarinenside E ( 6 ), iriflophenone-2- O -α- l -rhamnopyranoside ( 7 ), and iriflophenone-3- C -β-glucoside ( 8 ). The findings suggest the pharmacological potential of the crude extract (ALEX-M) and its isolates as natural anti-inflammatory agents, capable of suppressing NO production in RAW 264.7 cells stimulated by LPS/IFN-γ.

show abstract

The Heterogeneous Capacitated k-Center Problem

Cited by 7 publications

References 40 publications

Exponentially faster fixed-parameter algorithms for high-multiplicity scheduling

Exponentially faster fixed-parameter algorithms for high-multiplicity scheduling

Approximation Algorithm-Based Prosumer Scheduling for Microgrids

Phytochemical Constituents of Aquilaria malaccensis Leaf Extract and Their Anti-Inflammatory Activity against LPS/IFN-γ-Stimulated RAW 264.7 Cell Line

Contact Info

Product

Resources

About