Traditional Bin Packing Research Articles

Priority-based bin packing with subset constraints

This paper is concerned with a new variant of bin packing called priority-based bin packing with subset constraints (PBBP-SC). PBBP-SC is a variant of traditional bin packing (TBP). In a TBP instance, we are given a collection of items {t1,t2,…tn}, where each item ti has size si∈(0,1). The goal of TBP is to pack the items in as few unit-sized bins as possible. In a PBBP-SC instance, we are given a collection of n unit-size items and a collection of m bins of varying capacities. Associated with each item is a positive integer which is called its priority. The priority of an item indicates its importance in being included in a (possibly infeasible) packing. As with the traditional case, these items need to be packed in the fewest number of bins. What complicates the problem is the fact that each item can be assigned to only one of a select set of bins, i.e., the bins are not interchangeable. We investigate several problems associated with PBBP-SC. The first problem we study is the feasibility problem. This is the problem of checking if there is a feasible assignment to a given PBBP-SC instance. The second problem we study is the priority maximization problem. This is the problem of finding a maximum priority assignment of an infeasible PBBP-SC instance. The third problem we study is the bin minimization problem. This is the problem of finding an assignment with the fewest number of bins to pack all of the items in a feasible PBBP-SC instance. We derive a number of results from both the algorithmic and computational complexity perspectives for these problems. In particular, we show that both the feasibility and priority maximization problems are solvable in polynomial time. We also show that the bin minimization problem is log-APX-complete and cannot be solved in time o(1.41m) unless the Strong Exponential Time Hypothesis fails.

A study on load-balanced variants of the bin packing problem

We consider several extensions of the fractional bin packing problem, a relaxation of the traditional bin packing problem where the objects may be split across multiple bins. In these extensions, we introduce load-balancing constraints imposing that the share of each object which is assigned to a same bin must be equal. We propose a Mixed-Integer Programming (MIP) formulation and show that the problem becomes NP-hard if we limit to at most 3 the number of bins across which each object can be split.We then consider a variant where the balanced allocations of objects to bins may be done in successive rounds; this problem was inspired by telecommunication applications, and may be used to model simple Live Streaming networks. We show that two rounds are always sufficient to completely assign all objects to the bins and then provide an optimal polynomial-time allocation algorithm for this problem.

An Online Algorithm for Dynamic NFV Placement in Cloud-Based Autonomous Response Networks

Autonomous response networks are becoming a reality thanks to recent advances in cloud computing, Network Function Virtualization (NFV) and Software-Defined Networking (SDN) technologies. These enhanced networks fully enable autonomous real-time management of virtualized infrastructures. In this context, one of the major challenges is how virtualized network resources can be effectively placed. Although this issue has been addressed before in cloud-based environments, it is not yet completely resolved for the online placement of virtual machines. For such a purpose, this paper proposes an online heuristic algorithm called Topology-Aware Placement of Virtual Network Functions (TAP-VNF) as a low-complexity solution for such dynamic infrastructures. As a complement, we provide a general formulation of the network function placement using the service function chaining concept. Furthermore, two metrics called consolidation and aggregation validate the efficiency of the proposal in the experimental simulations. We have compared our approach with optimal solutions, in terms of consolidation and aggregation ratios, showing a more suitable performance for dynamic cloud-based environments. The obtained results show that TAP-VNF also outperforms existing approaches based on traditional bin packing schemes.

Multiagent-Based Resource Allocation for Energy Minimization in Cloud Computing Systems

Cloud computing has emerged as a very flexible service paradigm by allowing users to require virtual machine (VM) resources on-demand and allowing cloud service providers (CSPs) to provide VM resources via a pay-as-you-go model. This paper addresses the CSP’s problem of efficiently allocating VM resources to physical machines (PMs) with the aim of minimizing the energy consumption. Traditional energy-aware VM allocations either allocate VMs to PMs in a centralized manner or implement VM migrations for energy reduction without considering the migration cost in cloud computing systems. We address these two issues by introducing a decentralized multiagent (MA)-based VM allocation approach. The proposed MA works by first dispatching a cooperative agent to each PM to assist the PM in managing VM resources. Then, an auction-based VM allocation mechanism is designed for these agents to decide the allocations of VMs to PMs. Moreover, to tackle system dynamics and avoid incurring prohibitive VM migration overhead, a local negotiation-based VM consolidation mechanism is devised for the agents to exchange their assigned VMs for energy cost saving. We evaluate the efficiency of the MA approach by using both static and dynamic simulations. The static experimental results demonstrate that the MA can incur acceptable computation time to reduce system energy cost compared with traditional bin packing and genetic algorithm-based centralized approaches. In the dynamic setting, the energy cost of the MA is similar to that of benchmark global-based VM consolidation approaches, but the MA largely reduces the migration cost.

Partitioning bin-packing algorithms for distributed real-time systems

In this paper, we study extensions to bin packing algorithms to pack software modules into processors in real-time systems. We refer to this approach as Partitioning Bin-Packing. In this study, we analytically show that with partitioning bin-packing techniques the number of bins required by traditional bin packing can be reduced. We also evaluate heuristics to minimise both the number of processors (bins) needed and the network bandwidth required by communicating software modules that are partitioned across different processors. We find that a significant reduction in the number of bins is possible. Finally, different heuristics lead to different tradeoffs in processing vs. network needs.