Related papers: On-line Chain Partitioning Approach to Scheduling
Bin packing is an algorithmic problem that arises in diverse applications such as remnant inventory systems, shipping logistics, and appointment scheduling. In its simplest variant, a sequence of $T$ items (e.g., orders for raw material,…
For a given set of intervals on the real line, we consider the problem of ordering the intervals with the goal of minimizing an objective function that depends on the exposed interval pieces (that is, the pieces that are not covered by…
It is known that the First-Fit algorithm for partitioning a poset P into chains uses relatively few chains when P does not have two incomparable chains each of size k. In particular, if P has width w then Bosek, Krawczyk, and Szczypka (SIAM…
Scheduling is an important task allowing parallel systems to perform efficiently and reliably. For modern computation systems, divisible load is a special type of data which can be divided into arbitrary sizes and independently processed in…
In this paper, we proposed an effective approach for scheduling of multiprocessor unit time tasks with chain precedence on to large multiprocessor system. The proposed longest chain maximum processor scheduling algorithm is proved to be…
In the recent years, the scale of graph datasets has increased to such a degree that a single machine is not capable of efficiently processing large graphs. Thereby, efficient graph partitioning is necessary for those large graph…
Multicore shared cache processors pose a challenge for designers of embedded systems who try to achieve minimal and predictable execution time of workloads consisting of several jobs. To address this challenge the cache is statically…
Motivated by the Quality-of-Service (QoS) buffer management problem, we consider online scheduling of packets with hard deadlines in a finite capacity queue. At any time, a queue can store at most $b \in \mathbb Z^+$ packets. Packets arrive…
Sorting algorithms have attracted a great deal of attention and study, as they have numerous applications to Mathematics, Computer Science and related fields. In this thesis, we first deal with the mathematical analysis of the Quicksort…
In this thesis, we present fast deterministic algorithm to find small cuts in distributed networks. Finding small min-cuts for a network is essential for ensuring the quality of service and reliability. Throughout this thesis, we use the…
Partially ordered sets (posets) are fundamental combinatorial objects with important applications in computer science. Perhaps the most natural algorithmic task, given a size-$n$ poset, is to compute its number of linear extensions. In 1991…
We consider a parallel system of $m$ identical machines prone to unpredictable crashes and restarts, trying to cope with the continuous arrival of tasks to be executed. Tasks have different computational requirements (i.e., processing time…
Proportional apportionment is the problem of assigning seats to parties according to their relative share of votes. Divisor methods are the de-facto standard solution, used in many countries. In recent literature, there are two algorithms…
We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job…
In a capacitated directed graph, it is known that the set of all min-cuts forms a distributive lattice [1], [2]. Here, we describe this lattice as a regular predicate whose forbidden elements can be advanced in constant parallel time after…
Partitioning graphs into blocks of roughly equal size is widely used when processing large graphs. Currently there is a gap in the space of available partitioning algorithms. On the one hand, there are streaming algorithms that have been…
We consider the setting of online computation with advice, and study the bin packing problem and a number of scheduling problems. We show that it is possible, for any of these problems, to arbitrarily approach a competitive ratio of $1$…
Classical list scheduling is a very popular and efficient technique for scheduling jobs in parallel and distributed platforms. It is inherently centralized. However, with the increasing number of processors, the cost for managing a single…
We consider the Windows Scheduling problem. The problem is a restricted version of Unit-Fractions Bin Packing, and it is also called Inventory Replenishment in the context of Supply Chain. In brief, the problem is to schedule the use of…
We study web and mobile applications that are used to schedule advance service, from medical appointments to restaurant reservations. We model them as online weighted bipartite matching problems with non-stationary arrivals. We propose new…