Power Strip Packing of Malleable Demands in Smart Grid

We consider a problem of supplying electricity to a set of $\mathcal{N}$ customers in a smart-grid framework. Each customer requires a certain amount of electrical energy which has to be supplied during the time interval $[0,1]$. We assume that each demand has to be supplied without interruption, with possible duration between $\ell$ and $r$, which are given system parameters ($\ell\le r$). At each moment of time, the power of the grid is the sum of all the consumption rates for the demands being supplied at that moment. Our goal is to find an assignment that minimizes the {\it power peak} - maximal power over $[0,1]$ - while satisfying all the demands. To do this first we find the lower bound of optimal power peak. We show that the problem depends on whether or not the pair $\ell, r$ belongs to a "good" region $\mathcal{G}$. If it does - then an optimal assignment almost perfectly "fills" the rectangle $time \times power = [0,1] \times [0, A]$ with $A$ being the sum of all the energy demands - thus achieving an optimal power peak $A$. Conversely, if $\ell, r$ do not belong to $\mathcal{G}$, we identify the lower bound $\bar{A} >A$ on the optimal value of power peak and introduce a simple linear time algorithm that almost perfectly arranges all the demands in a rectangle $[0, A /\bar{A}] \times [0, \bar{A}]$ and show that it is asymptotically optimal

Empowering a helper cluster through data-width aware instruction selection policies

Narrow values that can be represented by less number of bits than the full machine width occur very frequently in programs. On the other hand, clustering mechanisms enable cost- and performance-effective scaling of processor back-end features. Those attributes can be combined synergistically to design special clusters operating on narrow values (a.k.a. helper cluster), potentially providing performance benefits. We complement a 32-bit monolithic processor with a low-complexity 8-bit helper cluster. Then, in our main focus, we propose various ideas to select suitable instructions to execute in the data-width based clusters. We add data-width information as another instruction steering decision metric and introduce new data-width based selection algorithms which also consider dependency, inter-cluster communication and load imbalance. Utilizing those techniques, the performance of a wide range of workloads are substantially increased; helper cluster achieves an average speedup of 11% for a wide range of 412 apps. When focusing on integer applications, the speedup can be as high as 22% on averagePeer ReviewedPostprint (published version

A satellite navigation system to improve the management of intermodal drayage

The intermodal transport chain can become more efficient by means of a good organization of the drayage movements. Drayage in intermodal container terminals involves the pick up or delivery of containers at customer locations, and the main objective is normally the assignment of transportation tasks to the different vehicles, often with the presence of time windows. The literature shows some works on centralised drayage management, but most of them consider the problem only from a static and deterministic perspective, whereas the work we present here incorporates the knowledge of the real-time position of the vehicles, which permanently enables the planner to reassign tasks in case the problem conditions change. This exact knowledge of position of the vehicles is possible thanks to a geographic positioning system by satellite (GPS, Galileo, Glonass), and the results show that this additional data can be used to dynamically improve the solution

Closing the Gap for Pseudo-Polynomial Strip Packing

Two-dimensional packing problems are a fundamental class of optimization problems and Strip Packing is one of the most natural and famous among them. Indeed it can be defined in just one sentence: Given a set of rectangular axis parallel items and a strip with bounded width and infinite height, the objective is to find a packing of the items into the strip minimizing the packing height. We speak of pseudo-polynomial Strip Packing if we consider algorithms with pseudo-polynomial running time with respect to the width of the strip. It is known that there is no pseudo-polynomial time algorithm for Strip Packing with a ratio better than 5/4 unless P = NP. The best algorithm so far has a ratio of 4/3 + epsilon. In this paper, we close the gap between inapproximability result and currently known algorithms by presenting an algorithm with approximation ratio 5/4 + epsilon. The algorithm relies on a new structural result which is the main accomplishment of this paper. It states that each optimal solution can be transformed with bounded loss in the objective such that it has one of a polynomial number of different forms thus making the problem tractable by standard techniques, i.e., dynamic programming. To show the conceptual strength of the approach, we extend our result to other problems as well, e.g., Strip Packing with 90 degree rotations and Contiguous Moldable Task Scheduling, and present algorithms with approximation ratio 5/4 + epsilon for these problems as well

Scheduling Monotone Moldable Jobs in Linear Time

A moldable job is a job that can be executed on an arbitrary number of processors, and whose processing time depends on the number of processors allotted to it. A moldable job is monotone if its work doesn't decrease for an increasing number of allotted processors. We consider the problem of scheduling monotone moldable jobs to minimize the makespan. We argue that for certain compact input encodings a polynomial algorithm has a running time polynomial in n and log(m), where n is the number of jobs and m is the number of machines. We describe how monotony of jobs can be used to counteract the increased problem complexity that arises from compact encodings, and give tight bounds on the approximability of the problem with compact encoding: it is NP-hard to solve optimally, but admits a PTAS. The main focus of this work are efficient approximation algorithms. We describe different techniques to exploit the monotony of the jobs for better running times, and present a (3/2+{\epsilon})-approximate algorithm whose running time is polynomial in log(m) and 1/{\epsilon}, and only linear in the number n of jobs

Wireless Backhaul Node Placement for Small Cell Networks

Small cells have been proposed as a vehicle for wireless networks to keep up with surging demand. Small cells come with a significant challenge of providing backhaul to transport data to(from) a gateway node in the core network. Fiber based backhaul offers the high rates needed to meet this requirement, but is costly and time-consuming to deploy, when not readily available. Wireless backhaul is an attractive option for small cells as it provides a less expensive and easy-to-deploy alternative to fiber. However, there are multitude of bands and features (e.g. LOS/NLOS, spatial multiplexing etc.) associated with wireless backhaul that need to be used intelligently for small cells. Candidate bands include: sub-6 GHz band that is useful in non-line-of-sight (NLOS) scenarios, microwave band (6-42 GHz) that is useful in point-to-point line-of-sight (LOS) scenarios, and millimeter wave bands (e.g. 60, 70 and 80 GHz) that are recently being commercially used in LOS scenarios. In many deployment topologies, it is advantageous to use aggregator nodes, located at the roof tops of tall buildings near small cells. These nodes can provide high data rate to multiple small cells in NLOS paths, sustain the same data rate to gateway nodes using LOS paths and take advantage of all available bands. This work performs the joint cost optimal aggregator node placement, power allocation, channel scheduling and routing to optimize the wireless backhaul network. We formulate mixed integer nonlinear programs (MINLP) to capture the different interference and multiplexing patterns at sub-6 GHz and microwave band. We solve the MINLP through linear relaxation and branch-and-bound algorithm and apply our algorithm in an example wireless backhaul network of downtown Manhattan.Comment: Invited paper at Conference on Information Science & Systems (CISS) 201