We study an on-line broadcast scheduling problem in which requests have deadlines, and the objective is to maximize the weighted throughput, i.e., the weighted total length of the satisfied requests. For the case where all requested pages have the same length, we present an online deterministic algorithm named BAR and prove that it is 4.56-competitive. This improves the previous algorithm of Kim and Chwa [11] which is shown to be 5-competitive by Chan et al. [4]. In the case that pages may have different lengths, we prove a lower bound of Ω(Δ/logΔ) on the competitive ratio where Δ is the ratio of maximum to minimum page lengths. This improves upon the previous $\sqrt{\Delta}$ lower bound in [11,4] and is much closer to the current upper bound of ($\Delta+2\sqrt{\Delta}+2$) in [7]. Furthermore, for small values of Δ we give better lower bounds.

Improved on-line broadcast scheduling with deadlines

Social networks often serve as a medium for the diffusion of ideas or innovations An individual's decision whether to adopt a product or innovation will be highly dependent on the choices made by the individual's peers or neighbors in the social network In this work, we study the game of innovation diffusion with multiple competing innovations such as when multiple companies market competing products using viral marketing Our first contribution is a natural and mathematically tractable model for the diffusion of multiple innovations in a network We give a (1-1/e) approximation algorithm for computing the best response to an opponent's strategy, and prove that the "price of competition" of this game is at most 2 We also discuss "first mover" strategies which try to maximize the expected diffusion against perfect competition Finally, we give an FPTAS for the problem of maximizing the influence of a single player when the underlying graph is a tree

Competitive influence maximization in social networks

Motivation: BUCKy is a C++ program that implements Bayesian concordance analysis. The method uses a non-parametric clustering of genes with compatible trees, and reconstructs the primary concordance tree from clades supported by the largest proportions of genes. A population tree with branch lengths in coalescent units is estimated from quartet concordance factors. Availability: BUCKy is open source and distributed under the GNU general public license at www.stat.wisc.edu/∼ane/bucky/. Contact: ane@stat.wisc.edu Supplementary information: Supplementary data are available at Bioinformatics online.

BUCKy: Gene tree/species tree reconciliation with Bayesian concordance analysis

The human brain is a topologically complex network embedded in anatomical space. Here, we systematically explored relationships between functional connectivity, complex network topology, and anatomical (Euclidean) distance between connected brain regions, in the resting-state functional magnetic resonance imaging brain networks of 20 healthy volunteers and 19 patients with childhood-onset schizophrenia (COS). Normal between-subject differences in average distance of connected edges in brain graphs were strongly associated with variation in topological properties of functional networks. In addition, a club or subset of connector hubs was identified, in lateral temporal, parietal, dorsal prefrontal, and medial prefrontal/cingulate cortical regions. In COS, there was reduced strength of functional connectivity over short distances especially, and therefore, global mean connection distance of thresholded graphs was significantly greater than normal. As predicted from relationships between spatial and topological properties of normal networks, this disorder-related proportional increase in connection distance was associated with reduced clustering and modularity and increased global efficiency of COS networks. Between-group differences in connection distance were localized specifically to connector hubs of multimodal association cortex. In relation to the neurodevelopmental pathogenesis of schizophrenia, we argue that the data are consistent with the interpretation that spatial and topological disturbances of functional network organization could arise from excessive "pruning" of short-distance functional connections in schizophrenia.

/pdf/the-anatomical-distance-of-functional-connections-predicts-9ttx38kx7p.pdf

The Anatomical Distance of Functional Connections Predicts Brain Network Topology in Health and Schizophrenia

Genome rearrangements have been modeled by a variety of operations such as inversions, translocations, fissions, fusions, transpositions and block interchanges. The double cut and join operation, introduced by Yancopoulos et al., allows to model all the classical operations while simplifying the algorithms. In this paper we show a simple way to apply this operation to the most general type of genomes with a mixed collection of linear and circular chromosomes. We also describe a graph structure that allows simplifying the theory and distance computation considerably, as neither capping nor concatenation of the linear chromosomes are necessary.

http://www.lifl.fr/SEQUOIA/MRI/20092010/articles/DCJBergeron.pdf

A unifying view of genome rearrangements

We study the following online preemptive scheduling problem: given a set of jobs with release times, deadlines, processing times and weights, schedule them so as to maximize the total value obtained. Unlike traditional scheduling problems, partially completed jobs can get partial values proportional to their amounts processed. Recently Chrobak et al. gave improved lower and upper bounds (1.236, 1.8) on the competitive ratio for this problem, the upper bound being achieved by using timesharing to simulate two equal-speed processors. In this paper we (1) give a new algorithm MIXED-k with competitive ratio 1/(1 − (k/(k + 1)) k ) which approaches e/(e−1) ≈ 1.582 when k →∞ , by using timesharing to simulate k equal-speed processors; (2) give an equivalent but much more practical algorithm MIX, which is e/(e − 1)-competitive (independent of k), by timesharing the processor with different speeds (depending on the job weights), and use its interesting properties to devise an efficient implementation; (3) improve the lower bound to 1.25 by showing an identical lower bound for randomized algorithms; and (4) prove a lower bound of 1.618 on the competitive ratio when timesharing is not allowed, thus answering an open problem raised by Chang and Yap, showing that timesharing provably helps in giving better algorithms for this problem.

/pdf/online-scheduling-with-partial-job-values-does-timesharing-7dn45pktw8.pdf

Online Scheduling with Partial Job Values: Does Timesharing or Randomization Help?

https://www.cs.ucr.edu/~marek/pubs/weightedthroughput.pdf

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. We also consider 2-uniform instances, where the span of each job is 2. We prove a lower bounds for randomized algorithms and deterministic memoryless algorithms. Finally, we consider the multiprocessor case and give an 1/(1 - (M M+1) M )-competitive algorithm for M processors. We also show improved lower bounds for the general and 2-uniform cases.

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.

Stanley P. Y. Fung

Papers

Improved on-line broadcast scheduling with deadlines

Online Scheduling with Partial Job Values: Does Timesharing or Randomization Help?

Online competitive algorithms for maximizing weighted throughput of unit jobs

Online competitive algorithms for maximizing weighted throughput of unit jobs

Online Competitive Algorithms for Maximizing Weighted Throughput of Unit Jobs