The k-Server with Preferences Problem

The famous $k$-Server Problem covers plenty of resource allocation scenarios, and several variations have been studied extensively. However, to the best of our knowledge, no research has considered the problem if the servers are not identical and requests can express which servers should serve them. Therefore, we present a new model generalizing the $k$-Server Problem by preferences of the requests and study it in uniform metrics for deterministic online algorithms. In our model, requests can either demand to be answered by any server (general requests) or by a specific one (specific requests). If only general requests appear, the instance is one of the $k$-Server Problem, and a lower bound for the competitive ratio of $k$ applies. If only specific requests appear, a competitive ratio of $1$ becomes trivial since there is no freedom regarding the servers' movements. We show that if both kinds of requests appear, the lower bound raises to $2k-1$. We study deterministic online algorithms in uniform metrics and present two algorithms. The first one has a competitive ratio dependent on the frequency of specific requests. It achieves a worst-case competitive ratio of $3k-2$ while it is optimal when only general or only specific requests appear (ratio of $k$ and $1$). The second has a close-to-optimal worst-case competitive ratio of $2k+14$. For the first algorithm, we show a lower bound of $3k-2$, while the second one has one of $2k-1$ when only general requests appear. Both algorithms differ in only one behavioral rule for each server that significantly influences the competitive ratio. Each server acting according to the rule allows approaching the worst-case lower bound, while it implies an increased lower bound for $k$-Server instances. Thus, there is a trade-off between performing well against instances of the $k$-Server Problem and ones containing specific requests.Comment: A conference version of this paper was accepted at the 34th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2022

Effects of flecainide on exercise-induced ventricular arrhythmias and recurrences in genotype-negative patients with catecholaminergic polymorphic ventricular tachycardia.

BACKGROUND: Conventional therapy with beta-blockers is incompletely effective in preventing arrhythmic events in patients with catecholaminergic polymorphic ventricular tachycardia (CPVT). We have previously discovered that flecainide in addition to conventional drug therapy prevents ventricular arrhythmias in patients with genotype-positive CPVT. OBJECTIVE: To study the efficacy of flecainide in patients with genotype-negative CPVT. METHODS: We studied the efficacy of flecainide for reducing ventricular arrhythmias during exercise testing and preventing arrhythmia events during long-term follow-up. RESULTS: Twelve patients with genotype-negative CPVT were treated with flecainide. Conventional therapy failed to control ventricular arrhythmias in all patients. Flecainide was initiated because of significant ventricular arrhythmias (n = 8), syncope (n = 3), or cardiac arrest (n = 1). At the baseline exercise test before flecainide, 6 patients had ventricular tachycardia and 5 patients had bigeminal or frequent ventricular premature beats. Flecainide reduced ventricular arrhythmias at the exercise test in 8 patients compared to conventional therapy, similar to that in patients with genotype-positive CPVT in our previous report. Notably, flecainide completely prevented ventricular arrhythmias in 7 patients. Flecainide was continued in all patients except for one who had ventricular tachycardia at the exercise test on flecainide. During a follow-up of 48±94 months, arrhythmia events (sudden cardiac death and aborted cardiac arrest) associated with noncompliance occurred in 2 patients. Flecainide was not discontinued owing to side effects in any of the patients. CONCLUSIONS: Flecainide was effective in patients with genotype-negative CPVT, suggesting that spontaneous Ca(2+) release from ryanodine channels plays a role in arrhythmia susceptibility, similar to that in patients with genotype-positive CPVT