Wun-Tat Chan

New Results on On-Demand Broadcasting with Deadline via Job Scheduling with Cancellation

This paper studies the on-demand broadcasting problem with deadlines. We give the first general upper bound and improve existing lower bounds on the competitive ratio of the problem. The novelty of our work is the introduction of a new job scheduling problem that allows cancellation. We prove that the broadcasting problem can be reduced to this scheduling problem. This reduction frees us from the complication of the broadcasting model and allows us to work on a conceptually simpler model for upper bound results.

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

Efficient Algorithms for Finding the Maximum Number of Disjoint Paths in Grids

\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 (

Escaping a grid by edge-disjoint paths

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

On-line scheduling of parallel jobs on two machines

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

On-line windows scheduling of temporary items

In a rectangular grid, given two sets of nodes, S (sources) and T (sinks), of size N2 each, the disjoint paths (DP) problem is to connect as many nodes in S to the nodes in T using a set of “disjoint” paths. (Both edge-disjoint and vertex-disjoint cases are considered in this paper.) Note that in this DP problem, a node in S can be connected to any node in T. Although in general the sizes of S and T do not have to be the same, algorithms presented in this paper can also find the maximum number of disjoint paths pairing nodes in S and T. We use the network flow approach to solve this DP problem. By exploiting all the properties of the network, such as planarity and regularity of a grid, integral flow, and unit capacity source/sink/flow, we can optimally compress the size of the working grid (to be defined) from O(N2) to O(N1.5) and solve the problem in O(N2.5) time for both the edge-disjoint and vertex-disjoint cases, an improvement over the straightforward approach which takes O(N3) time.

A Faster Algorithm for Finding Disjoint Paths in Grids

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

Dynamic bin packing of unit fractions items

O({\rm min}(r {\rm log} \ell, n \ell +r) {\rm log} {\rm log} n + Sort(n))