Online Knapsack Problems with a Resource Buffer

In this paper, we introduce online knapsack problems with a resource buffer. In the problems, we are given a knapsack with capacity 1, a buffer with capacity R >= 1, and items that arrive one by one. Each arriving item has to be taken into the buffer or discarded on its arrival irrevocably. When every item has arrived, we transfer a subset of items in the current buffer into the knapsack. Our goal is to maximize the total value of the items in the knapsack. We consider four variants depending on whether items in the buffer are removable (i.e., we can remove items in the buffer) or non-removable, and proportional (i.e., the value of each item is proportional to its size) or general. For the general&non-removable case, we observe that no constant competitive algorithm exists for any R >= 1. For the proportional&non-removable case, we show that a simple greedy algorithm is optimal for every R >= 1. For the general&removable and the proportional&removable cases, we present optimal algorithms for small R and give asymptotically nearly optimal algorithms for general R

NB-IoT via LEO satellites: An efficient resource allocation strategy for uplink data transmission

In this paper, we focus on the use of Low-Eart Orbit (LEO) satellites providing the Narrowband Internet of Things (NB-IoT) connectivity to the on-ground user equipment (UEs). Conventional resource allocation algorithms for the NBIoT systems are particularly designed for terrestrial infrastructures, where devices are under the coverage of a specific base station and the whole system varies very slowly in time. The existing methods in the literature cannot be applied over LEO satellite-based NB-IoT systems for several reasons. First, with the movement of the LEO satellite, the corresponding channel parameters for each user will quickly change over time. Delaying the scheduling of a certain user would result in a resource allocation based on outdated parameters. Second, the differential Doppler shift, which is a typical impairment in communications over LEO, directly depends on the relative distance among users. Scheduling at the same radio frame users that overcome a certain distance would violate the differential Doppler limit supported by the NB-IoT standard. Third, the propagation delay over a LEO satellite channel is around 4-16 times higher compared to a terrestrial system, imposing the need for message exchange minimization between the users and the base station. In this work, we propose a novel uplink resource allocation strategy that jointly incorporates the new design considerations previously mentioned together with the distinct channel conditions, satellite coverage times and data demands of various users on Earth. The novel methodology proposed in this paper can act as a framework for future works in the field.Comment: Tis work has been submitted to the IEEE IoT Journal for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Average Sensitivity of the Knapsack Problem

In resource allocation, we often require that the output allocation of an algorithm is stable against input perturbation because frequent reallocation is costly and untrustworthy. Varma and Yoshida (SODA\u2721) formalized this requirement for algorithms as the notion of average sensitivity. Here, the average sensitivity of an algorithm on an input instance is, roughly speaking, the average size of the symmetric difference of the output for the instance and that for the instance with one item deleted, where the average is taken over the deleted item. In this work, we consider the average sensitivity of the knapsack problem, a representative example of a resource allocation problem. We first show a (1-?)-approximation algorithm for the knapsack problem with average sensitivity O(?^{-1}log ?^{-1}). Then, we complement this result by showing that any (1-?)-approximation algorithm has average sensitivity ?(?^{-1}). As an application of our algorithm, we consider the incremental knapsack problem in the random-order setting, where the goal is to maintain a good solution while items arrive one by one in a random order. Specifically, we show that for any ? > 0, there exists a (1-?)-approximation algorithm with amortized recourse O(?^{-1}log ?^{-1}) and amortized update time O(log n+f_?), where n is the total number of items and f_? > 0 is a value depending on ?

The Online Simple Knapsack Problem with Reservation and Removability

In the online simple knapsack problem, a knapsack of unit size 1 is given and an algorithm is tasked to fill it using a set of items that are revealed one after another. Each item must be accepted or rejected at the time they are presented, and these decisions are irrevocable. No prior knowledge about the set and sequence of items is given. The goal is then to maximize the sum of the sizes of all packed items compared to an optimal packing of all items of the sequence. In this paper, we combine two existing variants of the problem that each extend the range of possible actions for a newly presented item by a new option. The first is removability, in which an item that was previously packed into the knapsack may be finally discarded at any point. The second is reservations, which allows the algorithm to delay the decision on accepting or rejecting a new item indefinitely for a proportional fee relative to the size of the given item. If both removability and reservations are permitted, we show that the competitive ratio of the online simple knapsack problem rises depending on the relative reservation costs. As soon as any nonzero fee has to be paid for a reservation, no online algorithm can be better than 1.5-competitive. With rising reservation costs, this competitive ratio increases up to the golden ratio (? ? 1.618) that is reached for relative reservation costs of 1-?5/3 ? 0.254. We provide a matching upper and lower bound for relative reservation costs up to this value. From this point onward, the tight bound by Iwama and Taketomi for the removable knapsack problem is the best possible competitive ratio, not using any reservations

A load-sharing architecture for high performance optimistic simulations on multi-core machines

In Parallel Discrete Event Simulation (PDES), the simulation model is partitioned into a set of distinct Logical Processes (LPs) which are allowed to concurrently execute simulation events. In this work we present an innovative approach to load-sharing on multi-core/multiprocessor machines, targeted at the optimistic PDES paradigm, where LPs are speculatively allowed to process simulation events with no preventive verification of causal consistency, and actual consistency violations (if any) are recovered via rollback techniques. In our approach, each simulation kernel instance, in charge of hosting and executing a specific set of LPs, runs a set of worker threads, which can be dynamically activated/deactivated on the basis of a distributed algorithm. The latter relies in turn on an analytical model that provides indications on how to reassign processor/core usage across the kernels in order to handle the simulation workload as efficiently as possible. We also present a real implementation of our load-sharing architecture within the ROme OpTimistic Simulator (ROOT-Sim), namely an open-source C-based simulation platform implemented according to the PDES paradigm and the optimistic synchronization approach. Experimental results for an assessment of the validity of our proposal are presented as well