Related papers: An All-Around Near-Optimal Solution for the Classi…
Motivated by bursty bandwidth allocation and by the allocation of virtual machines to servers in the cloud, we consider the online problem of packing items with random sizes into unit-capacity bins. Items arrive sequentially, but upon…
The stochastic matching problem deals with finding a maximum matching in a graph whose edges are unknown but can be accessed via queries. This is a special case of stochastic $k$-set packing, where the problem is to find a maximum packing…
Huang et al.~(STOC 2018) introduced the fully online matching problem, a generalization of the classic online bipartite matching problem in that it allows all vertices to arrive online and considers general graphs. They showed that the…
The online knapsack problem is a classic problem in the field of online algorithms. Its canonical version asks how to pack items of different values and weights arriving online into a capacity-limited knapsack so as to maximize the total…
We analyze the competitive ratio and the advice complexity of the online unbounded knapsack problem. An instance is given as a sequence of n items with a size and a value each, and an algorithm has to decide how often to pack each item into…
Packing cost accounts for a large part of the e-commerce logistics cost. Mining the patterns of customer orders and designing suitable packing bins help to reduce operating cost. In the classical bin packing problem, a given set of…
For bin packing, the input consists of $n$ items with sizes $s_1,...,s_n \in [0,1]$ which have to be assigned to a minimum number of bins of size 1. Recently, the second author gave an LP-based polynomial time algorithm that employed…
Imagine yourself moving to another place, and therefore, you need to pack all of your belongings into moving boxes with some capacity. In the classical bin packing model, you would try to minimize the number of boxes, knowing the exact size…
We continue the study of two recently introduced bin packing type problems, called bin packing with clustering, and online bin packing with delays. A bin packing input consists of items of sizes not larger than 1, and the goal is to…
We study the problem of maximizing a monotone submodular function subject to a Multiple Knapsack constraint. The input is a set $I$ of items, each has a non-negative weight, and a set of bins of arbitrary capacities. Also, we are given a…
Robotic-based compact storage and retrieval systems provide high-density storage in distribution center and warehouse applications. In the system, items are stored in bins, and the bins are organized inside a three-dimensional grid. Robots…
The knapsack problem is one of the classical problems in combinatorial optimization: Given a set of items, each specified by its size and profit, the goal is to find a maximum profit packing into a knapsack of bounded capacity. In the…
We introduce the strongly NP-complete pagination problem, an extension of BIN PACKING where packing together two items may make them occupy less volume than the sum of their individual sizes. To achieve this property, an item is defined as…
We present a packing-based approximation algorithm for the $k$-Set Cover problem. We introduce a new local search-based $k$-set packing heuristic, and call it Restricted $k$-Set Packing. We analyze its tight approximation ratio via a…
We present a simple randomized reduction from fully-dynamic integral matching algorithms to fully-dynamic "approximately-maximal" fractional matching algorithms. Applying this reduction to the recent fractional matching algorithm of…
Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seemingly escapes from the literature. A path containing at least $k$ vertices is considered long. When $k \le 3$, the…
Packing problems are an important class of optimization problems. The probably most well-known problem if this type is knapsack and many generalizations of it have been studied in the literature like Two-dimensional Geometric Knapsack…
This paper investigates a critical resource allocation problem in the first party cloud: scheduling containers to machines. There are tens of services and each service runs a set of homogeneous containers with dynamic resource usage;…
Cutting and packing problems are present in many, at first glance unconnected, areas, therefore it's beneficial to have a good understanding of their underlying structure, to select proper techniques for finding solutions. Cutting and…
In the Colored Bin Packing problem a set of items with varying weights and colors must be packed into bins of uniform weight limit such that no two items of the same color may be packed adjacently within a bin. We solve this problem for the…