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Papers by Chung Keung POON (COM)

Research paper thumbnail of Improved Randomized Online Scheduling of Intervals and Jobs

Theory of Computing Systems, 2013

We study the online preemptive scheduling of intervals and jobs (with restarts). Each interval or... more We study the online preemptive scheduling of intervals and jobs (with restarts). Each interval or job has an arrival time, a deadline, a length and a weight. The objective is to maximize the total weight of completed intervals or jobs. While the deterministic case for intervals was settled a long time ago, the randomized case remains open. In this paper we first give a 2-competitive randomized algorithm for the case of equal length intervals. The algorithm is barely random in the sense that it randomly chooses between two deterministic algorithms at the beginning and then sticks with it thereafter. Then we extend the algorithm to cover several other cases of interval scheduling including monotone instances, C-benevolent instances and D-benevolent instances, giving the same competitive ratio. These algorithms are surprisingly simple but have the best competitive ratio against all previous (fully or barely) randomized algorithms. Next we extend the idea to give a 3-competitive algorithm for equal length jobs. Finally, we prove a lower bound of 2 on the competitive ratio of all barely random algorithms that choose between two deterministic algorithms for scheduling equal length intervals (and hence jobs).

Research paper thumbnail of Improved on-line broadcast scheduling with deadlines

Journal of Scheduling, 2008

We study an on-line broadcast scheduling problem in which requests have deadlines, and the object... more 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 4.56competitive. 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(∆/ log ∆) on the competitive ratio where ∆ is the ratio of maximum to minimum page lengths. This improves upon the previous √ ∆ lower bound in [11, 4] and is much closer to the current upper bound of (∆ + 2 √ ∆ + 2) in [7]. Furthermore, for small values of ∆ we give better lower bounds.

Research paper thumbnail of Opportunistic data structures for range queries

Journal of Combinatorial Optimization, 2006

In this paper, we study the problem of supporting range sum queries on a compressed sequence of v... more In this paper, we study the problem of supporting range sum queries on a compressed sequence of values. For a sequence of n k-bit integers, k ≤ O(log n), our data structures require asymptotically the same amount of storage as the compressed sequence if compressed using the Lempel-Ziv algorithm. The basic structure supports range sum queries in O(log n) time. With an increase by a constant factor in the storage complexity, the query time can be improved to O(log log n + k).

Research paper thumbnail of On-demand Bounded Broadcast Scheduling with Tight Deadlines

We investigate a scheduling problem motivated by pull-based data delivering systems where there i... more We investigate a scheduling problem motivated by pull-based data delivering systems where there is a server keeping a number of pages; and clients requesting the same page can be satisfied simultaneously by one broadcast.

Research paper thumbnail of An approach towards automatic testing of student programs using token patterns

An approach towards automatic testing of student programs using token patterns

ABSTRACT Many universities use software systems to assess student programs by means of automatic ... more ABSTRACT Many universities use software systems to assess student programs by means of automatic testing, but most of these systems suffer from the technical limitation of requiring rigidly defined output formats. As such, a program that implements the correct algorithm is often rejected as incorrect due to minor non-conformance of its output. We propose a new approach to assessing the correctness of students' program outputs based on token patterns. Introduction To relieve the manual mundane tasks of assessing students' work in computer programming courses, many universities have developed software systems to automatically test students' programs by executing them with a set of test cases [1 – 4]. Most of these systems determine the correctness of a program by comparing its output to the correct output, often using the approach of direct character-by-character matching. This approach requires that the precise and detailed form of the output be given in the specification of the problem, and any slight deviation (such as an extra punctuation) will cause the match to fail. The demand of strict coherence to the required format is often regarded by students to be too harsh and is sometimes pedagogically unsatisfactory, for it may unnecessarily confine the way of implementation or indirectly disclose unintended hints to the solution [3, 4, 6, 7]. This paper briefly describes the problems with existing approaches (Section 1), proposes a new approach based on token patterns (Section 2), and outlines our further work (Section 3).

Research paper thumbnail of Tight Lower Bounds for st-Connectivity on the NNJAG Model

Siam Journal on Computing - SIAMCOMP, 1999

Directed st-connectivity is the problem of deciding whether or not there exists a path from a dis... more Directed st-connectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph. We prove a time- space lower bound on the probabilistic NNJAG model of Poon (Proc. 34th Annual Symposium on Foundations of Computer Science, Palo Alto, CA, 1993, pp. 218-227). Let n be the number of nodes in the input graph and S and T be the space and time used by the NNJAG, respectively. We show that, for any � > 0, if an NNJAG uses space S 2 O(n1−�), then T 2 2(log 2

Research paper thumbnail of Tight Lower Bounds For

Tight Lower Bounds For

. Directed st-connectivity is the problem of deciding whether or not there exists a path from a d... more . Directed st-connectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph. We prove a time-- space lower bound on the probabilistic NNJAG model of Poon [Proc. 34th Annual Symposium on Foundations of Computer Science, Palo Alto, CA, 1993, pp. 218--227]. Let n be the number of nodes in the input graph and S and T be the space and time used by the NNJAG, respectively. We show that, for any #>0, if an NNJAG uses space S # O(n 1-# ), then T # 2 #(log 2 (n/S)) ; otherwise T # 2 #(log 2 ( n log n S )/ log log n) (nS/ log n) 1/2 . (In a preliminary version of this paper by Edmonds and Poon [Proc. 27th Annual ACM Symposium on Theory of Computing, Las Vegas, NV, 1995, pp. 147--156.], a lower bound of T # 2 #(log 2 ( n log n S )/ log log n) (nS/ log n) 1/2 was proved.) Our result greatly improves the previous lower bound of ST # #(n 2 / log n) on the JAG model by Barnes and Ed...

Research paper thumbnail of Improved Randomized Online Scheduling of Intervals and Jobs

Theory of Computing Systems, 2013

We study the online preemptive scheduling of intervals and jobs (with restarts). Each interval or... more We study the online preemptive scheduling of intervals and jobs (with restarts). Each interval or job has an arrival time, a deadline, a length and a weight. The objective is to maximize the total weight of completed intervals or jobs. While the deterministic case for intervals was settled a long time ago, the randomized case remains open. In this paper we first give a 2-competitive randomized algorithm for the case of equal length intervals. The algorithm is barely random in the sense that it randomly chooses between two deterministic algorithms at the beginning and then sticks with it thereafter. Then we extend the algorithm to cover several other cases of interval scheduling including monotone instances, C-benevolent instances and D-benevolent instances, giving the same competitive ratio. These algorithms are surprisingly simple but have the best competitive ratio against all previous (fully or barely) randomized algorithms. Next we extend the idea to give a 3-competitive algorithm for equal length jobs. Finally, we prove a lower bound of 2 on the competitive ratio of all barely random algorithms that choose between two deterministic algorithms for scheduling equal length intervals (and hence jobs).

Research paper thumbnail of Improved on-line broadcast scheduling with deadlines

Journal of Scheduling, 2008

We study an on-line broadcast scheduling problem in which requests have deadlines, and the object... more 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 4.56competitive. 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(∆/ log ∆) on the competitive ratio where ∆ is the ratio of maximum to minimum page lengths. This improves upon the previous √ ∆ lower bound in [11, 4] and is much closer to the current upper bound of (∆ + 2 √ ∆ + 2) in [7]. Furthermore, for small values of ∆ we give better lower bounds.

Research paper thumbnail of Opportunistic data structures for range queries

Journal of Combinatorial Optimization, 2006

In this paper, we study the problem of supporting range sum queries on a compressed sequence of v... more In this paper, we study the problem of supporting range sum queries on a compressed sequence of values. For a sequence of n k-bit integers, k ≤ O(log n), our data structures require asymptotically the same amount of storage as the compressed sequence if compressed using the Lempel-Ziv algorithm. The basic structure supports range sum queries in O(log n) time. With an increase by a constant factor in the storage complexity, the query time can be improved to O(log log n + k).

Research paper thumbnail of On-demand Bounded Broadcast Scheduling with Tight Deadlines

We investigate a scheduling problem motivated by pull-based data delivering systems where there i... more We investigate a scheduling problem motivated by pull-based data delivering systems where there is a server keeping a number of pages; and clients requesting the same page can be satisfied simultaneously by one broadcast.

Research paper thumbnail of An approach towards automatic testing of student programs using token patterns

An approach towards automatic testing of student programs using token patterns

ABSTRACT Many universities use software systems to assess student programs by means of automatic ... more ABSTRACT Many universities use software systems to assess student programs by means of automatic testing, but most of these systems suffer from the technical limitation of requiring rigidly defined output formats. As such, a program that implements the correct algorithm is often rejected as incorrect due to minor non-conformance of its output. We propose a new approach to assessing the correctness of students' program outputs based on token patterns. Introduction To relieve the manual mundane tasks of assessing students' work in computer programming courses, many universities have developed software systems to automatically test students' programs by executing them with a set of test cases [1 – 4]. Most of these systems determine the correctness of a program by comparing its output to the correct output, often using the approach of direct character-by-character matching. This approach requires that the precise and detailed form of the output be given in the specification of the problem, and any slight deviation (such as an extra punctuation) will cause the match to fail. The demand of strict coherence to the required format is often regarded by students to be too harsh and is sometimes pedagogically unsatisfactory, for it may unnecessarily confine the way of implementation or indirectly disclose unintended hints to the solution [3, 4, 6, 7]. This paper briefly describes the problems with existing approaches (Section 1), proposes a new approach based on token patterns (Section 2), and outlines our further work (Section 3).

Research paper thumbnail of Tight Lower Bounds for st-Connectivity on the NNJAG Model

Siam Journal on Computing - SIAMCOMP, 1999

Directed st-connectivity is the problem of deciding whether or not there exists a path from a dis... more Directed st-connectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph. We prove a time- space lower bound on the probabilistic NNJAG model of Poon (Proc. 34th Annual Symposium on Foundations of Computer Science, Palo Alto, CA, 1993, pp. 218-227). Let n be the number of nodes in the input graph and S and T be the space and time used by the NNJAG, respectively. We show that, for any � > 0, if an NNJAG uses space S 2 O(n1−�), then T 2 2(log 2

Research paper thumbnail of Tight Lower Bounds For

Tight Lower Bounds For

. Directed st-connectivity is the problem of deciding whether or not there exists a path from a d... more . Directed st-connectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph. We prove a time-- space lower bound on the probabilistic NNJAG model of Poon [Proc. 34th Annual Symposium on Foundations of Computer Science, Palo Alto, CA, 1993, pp. 218--227]. Let n be the number of nodes in the input graph and S and T be the space and time used by the NNJAG, respectively. We show that, for any #>0, if an NNJAG uses space S # O(n 1-# ), then T # 2 #(log 2 (n/S)) ; otherwise T # 2 #(log 2 ( n log n S )/ log log n) (nS/ log n) 1/2 . (In a preliminary version of this paper by Edmonds and Poon [Proc. 27th Annual ACM Symposium on Theory of Computing, Las Vegas, NV, 1995, pp. 147--156.], a lower bound of T # 2 #(log 2 ( n log n S )/ log log n) (nS/ log n) 1/2 was proved.) Our result greatly improves the previous lower bound of ST # #(n 2 / log n) on the JAG model by Barnes and Ed...