Stanley P. Y. Fung

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

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.

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.

Improved on-line broadcast scheduling with deadlines

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

Linear-Time haplotype inference on pedigrees without recombinations

\sqrt{\Delta}

Efficient algorithms for finding a longest common increasing subsequence

lower bound in [11,4] and is much closer to the current upper bound of (

Lower bounds on online deadline scheduling with preemption penalties

\Delta+2\sqrt{\Delta}+2

Improved competitive algorithms for online scheduling with partial job values

) in [7]. Furthermore, for small values of Δ we give better lower bounds.

Improved Randomized Online Scheduling of Unit Length Intervals and Jobs

In this paper, a linear-time algorithm, which is optimal, is presented to solve the haplotype inference problem for pedigree data when there are no recombinations and the pedigree has no mating loops. The approach is based on the use of graphs to capture SNP, Mendelian and parity constraints of the given pedigree.

Laxity helps in broadcast scheduling

We study the problem of finding a longest common increasing subsequence (LCIS) of multiple sequences of numbers. The LCIS problem is a fundamental issue in various application areas, including the whole genome alignment. In this paper we give an efficient algorithm to find the LCIS of two sequences in