Tomáš Tichý

Improved online algorithms for buffer management in QoS switches

We consider the following buffer management problem arising in QoS networks: Packets with specified weights and deadlines arrive at a network switch and need to be forwarded so that the total weight of forwarded packets is maximized. Packets not forwarded before their deadlines are lost. The main result of the article is an online 64/33 ≈ 1.939-competitive algorithm, the first deterministic algorithm for this problem with competitive ratio below 2. For the 2-uniform case we give an algorithm with ratio ≈ 1.377 and a matching lower bound.

Online Competitive Algorithms for Maximizing Weighted Throughput of Unit Jobs

We study an online scheduling problem for unit-length jobs, where each job is specified by its release time, deadline, and a nonnegative weight. The goal is to maximize the weighted throughput, that is the total weight of scheduled jobs. We first give a randomized algorithm RMix with competitive ratio of e/(e-1)≈ 1.582. Then we consider s-bounded instances where the span of each job is at most s. We give a 1.25-competitive randomized algorithm for 2-bounded instances, and a deterministic algorithm Edf α , whose competitive ratio on s-bounded instances is at most 2-2/s+o(1/s). For 3-bounded instances its ratio is φ ≈ 1.618, matching the lower bound.

Preemptive scheduling in overloaded systems

The following scheduling problem is studied: We are given a set of tasks with release times, deadlines, and profit rates. The objective is to determine a 1-processor preemptive schedule of the given tasks that maximizes the overall profit. In the standard model, each completed task brings profit, while noncompleted tasks do not. In the metered model, a task brings profit proportional to the execution time even if not completed. For the metered task model, we present an efficient offline algorithm and improve both the lower and upper bounds on the competitive ratio of online algorithms. Furthermore, we prove three lower bound results concerning resource augmentation in both models.

Improved Online Algorithms for Buffer Management in QoS Switches

The following buffer management problem is studied: packets with specified weights and deadlines arrive at a network switch and need to be forwarded so that the total weight of forwarded packets is maximized. A packet not forwarded before its deadline brings no profit. The main result is an online \(\frac{64}{33}\approx 1.939\)-competitive algorithm, the first deterministic algorithm for this problem with competitive ratio below 2. In the s-uniform case, where for all packets the deadline equals the arrival time plus s, we give an \({5}-\sqrt{10} \approx 1.838\)-competitive algorithm. This algorithm achieves the same ratio in a more general scenario when all packets are similarly ordered. For the 2-uniform case we give an algorithm with ratio ≈ 1.377 and a matching lower bound.

Synthesis of ester prodrugs of 9-(S)-[3-hydroxy-2-(phosphonomethoxy)propyl]-2,6-diaminopurine (HPMPDAP) as anti-poxvirus agents.

9-(S)-[3-Hydroxy-2-(phosphonomethoxy)propyl]-2,6-diaminopurine (HPMPDAP) and its cyclic form were selected for further evaluation as potential drug candidates against poxvirus infections. To increase bioavailability of these compounds, synthesis of their structurally diverse ester prodrugs was carried out: alkoxyalkyl (hexadecyloxypropyl, octadecyloxyethyl, hexadecyloxyethyl), pivaloyloxymethyl (POM), 2,2,2-trifluoroethyl, butylsalicylyl, and prodrugs based on peptidomimetics. Most HPMPDAP prodrugs were synthesized in the form of monoesters as well as the corresponding cyclic phosphonate esters. The activity was evaluated not only against vaccinia virus but also against different herpes viruses. The most potent and active prodrugs against vaccinia virus were the alkoxyalkyl ester derivatives of HPMPDAP, with 50% effective concentrations 400-600-fold lower than those of the parent compound. Prodrugs based on peptidomimetics, the 2,2,2-trifluoroethyl, the POM, and the butylsalicylyl derivatives, were able to inhibit vaccinia virus replication at 50% effective concentrations that were equivalent or ∼10-fold lower than those observed for the parent compounds.

Online Scheduling of Equal-Length Jobs: Randomization and Restarts Help

The input of the studied scheduling problem is a set of jobs with equal processing times, where each job is specified by its release time and deadline. The goal is to determine a single-processor, non-preemptive schedule that maximizes the number of completed jobs. In the online version, each job arrives at its release time.

Randomized strategies for the plurality problem

We consider a game played by two players, Paul and Carol. At the beginning of the game, Carol fixes a coloring of n balls. At each turn, Paul chooses a pair of the balls and asks Carol whether the balls have the same color. Carol truthfully answers his question. Pauls goal is to determine the most frequent (plurality) color in the coloring by asking as few questions as possible. The game is studied in the probabilistic setting when Paul is allowed to choose his next question randomly. We give asymptotically tight bounds both for the case of two colors and many colors. For the balls colored by k colors, we prove a lower bound @W(kn) on the expected number of questions; this is asymptotically optimal. For the balls colored by two colors, we provide a strategy for Paul to determine the plurality color with the expected number of 2n/3+O(nlogn) questions; this almost matches the lower bound 2n/3-O(n).

New prodrugs of Adefovir and Cidofovir

Abstract New Adefovir (PMEA) prodrugs with a pro-moiety consisting of decyl or decyloxyethyl chain bearing hydroxyl function(s), hexaethyleneglycol or a (5-methyl-2-oxo-1,3-dioxolen-4-yl)methyl unit were prepared starting from the tetrabutylammonium salt of the phosphonate drug and an appropriate alkyl bromide or tosylate. Analogously, two esters of Cidofovir [(S)-HPMPC] bearing a hexaethyleneglycol moiety were prepared. The activity of the prodrugs was evaluated in vitro against different virus families. A loss in the antiviral activities of the hydroxylated decyl or decyloxyethyl esters and hexaethyleneglycol esters of PMEA against human immunodeficiency virus (HIV) and herpesviruses [including herpes simplex virus (HSV), varicella-zoster virus (VZV), and human cytomegalovirus (CMV)] occurred in comparison with the parent compound. On the other hand, the (5-methyl-2-oxo-1,3-dioxolen-4-yl)methyl ester of PMEA showed significant activities against HIV and herpesviruses. (S)-HPMPC prodrugs exhibited anti-cytomegalovirus activities in the same range as the parent drug, whereas the anti-HSV and anti-VZV activities were one- to seven-fold lower than that of Cidofovir.

Preemptive Scheduling in Overloaded Systems

The following scheduling problem is studied: We are given a set of tasks withrelease times, deadlines, and profit rates. The objective is to determine a 1-processor preemptive schedule of the given tasks that maximizes the overall profit. In the standard model, each completed task brings profit, while non-completed tasks do not. In the metered model, a task brings profit proportional to the execution time even if not completed. For the metered task model, we present an efficient offline algorithm and improve both the lower and upper bounds on the competitive ratio of online algorithms. Furthermore, we prove three lower bound results concerning resource augmentation in both models.

Discovery of Orally Available Prodrugs of the Glutamate Carboxypeptidase II (GCPII) Inhibitor 2-Phosphonomethylpentanedioic Acid (2-PMPA)

2-Phosphonomethylpentanedioic acid (1, 2-PMPA) is a potent inhibitor of glutamate carboxypeptidase II which has demonstrated robust neuroprotective efficacy in many neurological disease models. However, 1 is highly polar containing a phosphonate and two carboxylates, severely limiting its oral bioavailability. We strategized to mask the polar groups via a prodrug approach, increasing the likelihood of passive oral absorption. Our initial strategy was to cover the phosphonate with hydrophobic moieties such as pivaloyloxymethyl (POM) and isopropyloxycarbonyloxymethyl (POC) while keeping the α- and γ-carboxylates unsubstituted. This attempt was unsuccessful due to the chemical instability of the bis-POC/POM derivatives. Addition of α,γ-diesters and α-monoesters enhanced chemical stability and provided excellent oral exposure in mice, but these mixed esters were too stable in vivo, resulting in minimal release of 1. By introducing POC groups on both the phosphonate and α-carboxylate, we synthesized Tris-POC-2-PMPA (21b), which afforded excellent release of 1 following oral administration in both mice and dog.