Related papers: A new lower bound for classic online bin packing
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,…
We break the barrier of $3/2$ for the problem of online load balancing with known makespan, also known as bin stretching. In this problem, $m$ identical machines and the optimal makespan are given. The load of a machine is the total size of…
We study the discrete bin covering problem where a multiset of items from a fixed set $S \subseteq (0,1]$ must be split into disjoint subsets while maximizing the number of subsets whose contents sum to at least $1$. We study the online…
We explore a novel theoretical model for studying the performance of distributed storage management systems where the data-centers have limited capacities (as compared to storage space requested by the users). Prior schemes such as…
A variant of the online knapsack problem is considered in the settings of trusted and untrusted predictions. In Unit Profit Knapsack, the items have unit profit, and it is easy to find an optimal solution offline: Pack as many of the…
In the problem of online load balancing on uniformly related machines with bounded migration, jobs arrive online one after another and have to be immediately placed on one of a given set of machines without knowledge about jobs that may…
We study a variant of online bin packing, called colorful bin packing. In this problem, items that are presented one by one are to be packed into bins of size 1. Each item i has a size s_i \in [0,1] and a color c_i \in C, where C is a set…
Online bidding is a classical problem in online decision-making, with applications in resource allocation, hierarchical clustering, and the analysis of approximation algorithms. We study its randomized learning-augmented variant, where an…
We study a two-dimensional generalization of the classical Bin Packing problem, denoted as 2D Demand Bin Packing. In this context, each bin is a horizontal timeline, and rectangular tasks (representing electric appliances or computational…
The bottom-left algorithm is a simple heuristic for the Strip Packing Problem. It places the rectangles in the given order at the lowest free position in the strip, using the left most position in case of ties. Despite its simplicity, the…
In 2005 Li et al. gave a phi-competitive deterministic online algorithm for scheduling of packets with agreeable deadlines with a very interesting analysis. This is known to be optimal due to a lower bound by Hajek. We claim that the…
We present deterministic and randomized algorithms for the problem of online packet routing in grids in the competitive network throughput model \cite{AKOR}. In this model the network has nodes with bounded buffers and bounded link…
Consider a storage area where arriving items are stored temporarily in bounded capacity stacks until their departure. We look into the problem of deciding where to put an arriving item with the objective of minimizing the maximum number of…
The online stochastic matching problem was introduced by [FMMM09], together with the $(1-\frac1e)$-competitive Suggested Matching algorithm. In the most general edge-weighted setting, this ratio has not been improved for more than one…
In the knapsack problem, we are given a knapsack of some capacity and a set of items, each with a size and a value. The goal is to pack a selection of these items fitting the knapsack that maximizes the total value. The online version of…
We study the problem of online unweighted bipartite matching with $n$ offline vertices and $n$ online vertices where one wishes to be competitive against the optimal offline algorithm. While the classic RANKING algorithm of Karp et al.…
We consider the open, non-preemptive online Dial-a-Ride problem on the real line, where transportation requests appear over time and need to be served by a single server. We give a lower bound of 2.0585 on the competitive ratio, which is…
We study the $b$-matching problem in bipartite graphs $G=(S,R,E)$. Each vertex $s\in S$ is a server with individual capacity $b_s$. The vertices $r\in R$ are requests that arrive online and must be assigned instantly to an eligible server.…
We consider competitive algorithms for adaptive group testing problems. In the first part of the paper, we develop an algorithm with competitive constant c < 1.452 thus improving the up to now best known algorithms with constants…
The online unit clustering problem was proposed by Chan and Zarrabi-Zadeh (WAOA2007 and Theory of Computing Systems 45(3), 2009), which is defined as follows: "Points" are given online in the $d$-dimensional Euclidean space one by one. An…