In the (1-dimensional) bin packing problem, we are asked to pack all the given items into bins, each of capacity one, so that the number of non-empty bins is minimized. Zhu [Chaos, Solitons & Fractals 2016] proposed an approximation algorithm MM that sorts the item sequence in a non-increasing order by size at the beginning, and then repeatedly packs, into the current single open bin, first as many of the largest items in the remaining sequence as possible and then as many of the smallest items in the remaining sequence as possible. In this paper we prove that the asymptotic approximation ratio of MM is at most 1.5. Next, focusing on the fact that MM is at the intersection of two algorithm classes, max-min algorithms and 1-bounded space algorithms, we comprehensively analyze the theoretical performance bounds of each subclass derived from the two classes. Our results include a lower bound of 1.25 for the intersection of the two classes. Furthermore, we extend the theoretical analysis over algorithm classes to the cardinality constrained bin packing problem.

Interacting with the touchscreen of a mobile phone in virtual reality (VR) is challenging because users cannot see their fingers when aiming for targets. We propose using two mirrors reflecting the front camera of the phone and a purpose-built deep neural network to infer the 3D position of fingertips above the screen. Network training is self-supervised after only a few hundred initial labelled images and does not require any external sensor. The inferred fingertip positions can be used to control different hand models and objects in VR. Controlled experiments evaluate tracking performance for single-finger touch input, and compare several 3D hand representations with a flat 2D overlay used in previous work. The results confirm the suitability of our fingertip tracker to aid precise tapping of small targets on the phone screen and provide insights about the effect of various hand representations on control and presence. Finally, we provide several application examples showing how 3D fingertip input can complement and extend phone-based touch interaction in VR.

Abstract. We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation measured on an arc of the boundary, we propose a numerical algorithm to recover the source in the convex hull of this arc. The method involves an unstable step of inverting a bounded operator whose range is not closed. We show that the continuity constant of the discretized inverse grows at most linearly with the discretization step, thus stabilizing the problem. Numerical examples presented show the effectiveness of the proposed method.

Smartphone touch screens are potentially attractive for interaction in virtual reality (VR). However, the user cannot see the phone or their hands in a fully immersive VR setting, impeding their ability for precise touch input. We propose mounting a mirror above the phone screen such that the front-facing camera captures the thumbs on or near the screen. This enables the creation of semi-transparent overlays of thumb shadows and inference of fingertip hover points with deep learning, which help the user aim for targets on the phone. A study compares the effect of visual feedback on touch precision in a controlled task and qualitatively evaluates three example applications demonstrating the potential of the technique. The results show that the enabled style of feedback is effective for thumb-size targets, and that the VR experience can be enriched by using smartphones as VR controllers supporting precise touch input.

We consider the two dimensional quantitative imaging problem of recovering a radiative source inside an absorbing and scattering medium from knowledge of the outgoing radiation measured at the boundary. The medium has an anisotropic scattering property that is neither negligible nor large enough for the diffusion approximation to hold. We present the numerical realization of the authors' recently proposed reconstruction method. For scattering kernels of finite Fourier content in the angular variable, the solution is exact. The feasibility of the proposed algorithms is demonstrated in several numerical experiments, including simulated scenarios for parameters meaningful in optical molecular imaging.

We study scheduling problems in battery-operated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadline-based settings, in this article we are interested in schedules that guarantee good response times. More specifically, our goal is to schedule a sequence of jobs on a variable-speed processor so as to minimize the total cost consisting of the energy consumption and the total flow time of all jobs. We first show that when the amount of work, for any job, may take an arbitrary value, then no online algorithm can achieve a constant competitive ratio. Therefore, most of the article is concerned with unit-size jobs. We devise a deterministic constant competitive online algorithm and show that the offline problem can be solved in polynomial time.

After many years of intensive deliberation, an international low-bit-rate video coding standard, known as CCITT (International Telegraph and Telephone Consultative Committee) Recommendation H.261, has been completed. The H.261 covers a wide range of bit rates at p*64 kbs, where p=1, 2, . . ., 30. A great deal of real-time signal processing power is required to compress an NTSC or other similar video signals to these rates for transport and to reconstruct the original signal back for display. In order to demonstrate the video quality of the newly established standard and the feasibility of a cost-effective VLSI solution, a real-time video codec based on H.261 has been constructed using ASICs (application specific integrated circuits). A single-board research prototype consisting of 11 ASICs with an aggregate signal processing power of approximately two billion operations per second is presented.>

The Discrete Cosine Transform (DCT) is considered to be the most effective transform coding technique for image and video compression. In this paper, a new implementation of an experimental prototype multi-function DCT/IDCT (Inverse DCT) chip is reported. The chip is based on a distributed arithmetic architecture. The main features of the chip include: 1) The DCT and the IDCT are integrated in the same chip, 2) the chip achieves high accuracy, exceeding the stringent requirements of a proposed CCITF standard, 3) it achieves a high operating speed of 27 MHz, and is thus applicable to a wide-range of real-time image and video applications, 4) the internal clock frequency is the same as the pixel rate, and 5) with an on-chip zigzag scan converter and an adder/subtractor, it is multifunctional and useful in a DPCM configuration. The chip is implemented with standard cells and contains about 156k transistors.