Searcharxiv⌕ Search

arXiv subjects

Gruia Calinescu

Publications and source records attributed to Gruia Calinescu.

4 recordsLinked to original sources
arXiv2026

Online Flexible Busy Time Scheduling on Heterogeneous Machines

We study the online busy time scheduling model on heterogeneous machines. In our setting, jobs with uniform processing time arrive online with a deadline that becomes known to the algorithm at the job's arrival time. An algorithm has access to machines, each with different associated capacities and costs. The goal is to schedule jobs on machines by their deadline, so that the total cost incurred by the scheduling algorithm is minimized. While busy time scheduling has been well-studied, relatively little is known when machines are heterogeneous (i.e., have different costs and capacities), despite this natural theoretical generalization being the most practical model for clients using cloud computing services. We make significant progress in understanding this model by designing a deterministic online algorithm with competitive ratio 8(2p-1)/p < 16 when all jobs have uniform processing time p. A randomized version of this algorithm is 4(2p-1)/(p \ln 2)-competitive against an oblivious adversary. For unit-processing-time jobs, we give lower bounds of 4 and e (where e is Euler's number) on the competitive ratio of deterministic and randomized online algorithms, respectively. For unit-processing-time jobs with agreeable deadlines, we provide a deterministic 2-competitive online algorithm and a matching lower bound.

cs.DS↗
arXiv2026

On Randomized Online Span Minimization

We study the online Busy Time scheduling model on a single machine of unbounded capacity, with non-preemptive jobs. In our setting, flexible jobs arrive online with a processing time and deadline, both of which become known to the algorithm at the job's arrival time. The goal is to schedule jobs on the machine to finish all jobs by their deadlines, so that the total time when the machine is turned on (busy time, also called span in this setting) is minimized. We present a randomized online algorithm with an exact competitive ratio of exactly (1 + e) < 3.72, where e is Euler's number, against an oblivious adversary, and show that no randomized algorithm can have a competitive ratio better than $e$ against an oblivious adversary. This lower bound holds even for algorithms that are allowed to restart jobs and are given lookahead. Previous work either dealt with special cases, or with deterministic algorithms, for which the known upper bound on the competitive ratio is 5 and the known lower bound is 4. Our findings offer fresh insights into randomization in online energy-aware scheduling. In the setting where jobs have uniform processing times, and a job that is started by the algorithm must be finished, we show that no deterministic algorithm can do better than 2, even when the jobs are agreeable. This deterministic lower bound also holds for uniform processing times and restarts in the scenario where a job's deadline is only revealed at its starting deadline. For Capacitated Busy Time with p_max-lookahead, we obtain a deterministic online algorithm with competitive ratio at most 8 and a randomized online algorithm with competitive ratio at most (4+ e) < 6.72, against an oblivious adversary.

cs.DS↗
arXiv2012

1.85 Approximation for Min-Power Strong Connectivity

Given a directed simple graph G=(V,E) and a nonnegative-valued cost function the power of a vertex u in a directed spanning subgraph H is given by the maximum cost of an arcs of H exiting u. The power of H is the sum of the power of its vertices. Power Assignment seeks to minimize the power of H while H satisfies some connectivity constraint. In this paper, we assume E is bidirected (for every directed edge e in E, the opposite edge exists and has the same cost), while H is required to be strongly connected. This is the original power assignment problem introduced by Chen and Huang in 1989, who proved that bidirected minimum spanning tree has approximation ratio at most 2 (this is tight). In Approx 2010, we introduced a Greedy approximation algorithm and claimed a ratio of 1.992. Here we improve the analysis to 1.85. The proof also shows that a natural linear programming relaxation, introduced by us in 2012, has the same 1.85 integrality gap.

cs.DS↗