Motivated by settings such as medical treatments or aircraft maintenance, we consider a scheduling problem with jobs that consist of two operations, a test and a processing part. The time required to execute the test is known in advance while the time required to execute the processing part becomes known only upon completion of the test. We use competitive analysis to study algorithms for minimizing the sum of completion times for $n$ given jobs on a single machine. As our main result, we prove using a novel analysis technique that the natural $1$-SORT algorithm has competitive ratio at most 1.861. For the special case of uniform test times, we show that a simple threshold-based algorithm has competitive ratio at most 1.585. We also prove a lower bound that shows that no deterministic algorithm can be better than $\sqrt{2}$-competitive even in the case of uniform test times.

In this paper, we consider a primal-dual algorithmic aspect of the link scheduling problem in dynamic wireless networks, where the channel characteristics are dramatically time-varying that could render state-of-the-art link scheduling mechanisms computational expensive to fit network dynamics. Building upon the optimality condition of treating interference as noise, we formulate link scheduling as a maximum weighted clique problem on a coexisting graph, which can be transformed into a minimum weighted vertex coloring problem (MWVCP) through the primal-dual technique. With an adversarial perturbation modeling of network dynamics with edge insertion/deletion, we propose dynamic graph algorithms to solve the MWVCP for chordal graph classes with theoretical guarantees on algorithmic feasibility, optimality, and updating complexity. It is expected the resulting link scheduling mechanism could shed light on robust, scalable, and certifiable system designs in dynamic wireless networks from the algorithmic perspective.

We investigate the power-down mechanism which decides when a machine transitions between states such that the total energy consumption, characterized by execution cost, idle cost and switching cost, is minimized. In contrast to most of the previous studies on the offline model, we focus on the online model in which a sequence of jobs with their release time, execution time and deadline, arrive in an online fashion. More precisely, we exploit a different switching on and off strategy and present an upper bound of 3, and further show a lower bound of 2.1, in a dual-machine model, introduced by Chen et al. in 2014 [STACS 2014: 226-238], both of which beat the currently best result.

In this paper, we consider the topological interference management (TIM) problem in a dynamic setting, where an adversary perturbs network topology to prevent the exploitation of sophisticated coding opportunities (e.g., interference alignment). Focusing on a special class of network topology – chordal networks – we investigate algorithmic aspects of the TIM problem under adversarial topology perturbation. In particular, given the adversarial perturbation with respect to edge insertion/deletion, we propose a dynamic graph coloring algorithm that allows for a constant number of re-coloring updates against each inserted/deleted edge to achieve the information-theoretic optimality. This is a sharp reduction of the general graph re-coloring, whose optimal number of updates scales as the size of the network, thanks to the delicate exploitation of the structural properties of chordal graph classes.

The online car-sharing problem finds many real-world applications. The problem, proposed by Luo, Erlebach and Xu in 2018, mainly focuses on an online model in which there are two locations: 0 and 1, and k total cars. Each request which specifies its pick-up time and pick-up location (among 0 and 1, and the other is the drop-off location) is released in each stage a fixed amount of time before its specified start (i.e. pick-up) time. The time between the booking (i.e. released) time and the start time is enough to move empty cars between 0 and 1 for relocation if they are not used in that stage. The model, called k S2L-F, assumes that requests in each stage arrive sequentially regardless of the same booking time and the decision (accept or reject) must be made immediately. The goal is to accept as many requests as possible. In spite of only two locations, the analysis does not seem easy and the (tight) competitive ratio (CR) is only known to be 2 for k = 2 and 1.5 for a restricted value of k , i.e., a multiple of three. In this paper, we remove all the holes of unknown CR's; namely we prove that the CR is 2 k k + ⌊ k / 3 ⌋ for all k ≥ 2 . Furthermore, if the algorithm can delay its decision until all requests have come in each stage, the CR is improved to roughly 4/3. We can take this advantage even further; precisely we can achieve a CR of 2 + R 3 if the number of requests in each stage is at most Rk , 1 ≤ R ≤ 2 , where we do not have to know the value of R in advance. Finally we demonstrate that randomization also helps to get (slightly) better CR's, and prove some lower bounds to show the tightness.

In this paper, we consider the topological interference management (TIM) problem in a dynamic setting, where an adversary perturbs network topology to prevent the exploitation of sophisticated coding opportunities (e.g., interference alignment). Focusing on a special class of network topology - chordal networks - we investigate algorithmic aspects of the TIM problem under adversarial topology perturbation. In particular, given the adversarial perturbation with respect to edge insertion/deletion, we propose a dynamic graph coloring algorithm that allows for a constant number of re-coloring updates against each inserted/deleted edge to achieve the information-theoretic optimality. This is a sharp reduction of the general graph re-coloring, whose optimal number of updates scales as the size of the network, thanks to the delicate exploitation of the structural properties of chordal graph classes.