Related papers: Generalized Assignment and Knapsack Problems in th…
We consider the problem of maximizing a fractionally subadditive function under a knapsack constraint that grows over time. An incremental solution to this problem is given by an order in which to include the elements of the ground set, and…
Matching problems with group-fairness constraints and diversity constraints have numerous applications such as in allocation problems, committee selection, school choice, etc. Moreover, online matching problems have lots of applications in…
In this paper the following selection problem is discussed. A set of $n$ items is given and we wish to choose a subset of exactly $p$ items of the minimum total cost. This problem is a special case of 0-1 knapsack in which all the item…
Knapsack problem (KP) is a representative combinatorial optimization problem that aims to maximize the total profit by selecting a subset of items under given constraints on the total weights. In this study, we analyze a generalized version…
We study \emph{parallel} online algorithms: For some fixed integer $k$, a collective of $k$ parallel processes that perform online decisions on the same sequence of events forms a $k$-\emph{copy algorithm}. For any given time and input…
Can one choose a good Huffman code on the fly, without knowing the underlying distribution? Online Slot Allocation (OSA) models this and similar problems: There are n slots, each with a known cost. There are n items. Requests for items are…
We consider a selfish variant of the knapsack problem. In our version, the items are owned by agents, and each agent can misrepresent the set of items she owns---either by avoiding reporting some of them (understating), or by reporting…
We propose a new approach to competitive analysis in online scheduling by introducing the novel concept of competitive-ratio approximation schemes. Such a scheme algorithmically constructs an online algorithm with a competitive ratio…
In this work, we study the classic submodular maximization problem under knapsack constraints and beyond. We first present an $(7/16-\varepsilon)$-approximate algorithm for single knapsack constraint, which requires…
The problem of selecting a small-size representative summary of a large dataset is a cornerstone of machine learning, optimization and data science. Motivated by applications to recommendation systems and other scenarios with query-limited…
We study the non-uniform capacitated multi-item lot-sizing (\lotsizing) problem. In this problem, there is a set of demands over a planning horizon of $T$ time periods and all demands must be satisfied on time. We can place an order at the…
We study the online facility location problem with uniform facility costs in the random-order model. Meyerson's algorithm [FOCS'01] is arguably the most natural and simple online algorithm for the problem with several advantages and…
Online allocation problems with resource constraints are central problems in revenue management and online advertising. In these problems, requests arrive sequentially during a finite horizon and, for each request, a decision maker needs to…
We study online capacitated resource allocation, a natural generalization of online stochastic max-weight bipartite matching. This problem is motivated by ride-sharing and Internet advertising applications, where online arrivals may have…
Natural selection drives species to develop brains, with sizes that increase with the complexity of the tasks to be tackled. Our goal is to investigate the balance between the metabolic costs of larger brains compared to the advantage they…
We propose a novel technique for algorithm-selection, applicable to optimisation domains in which there is implicit sequential information encapsulated in the data, e.g., in online bin-packing. Specifically we train two types of recurrent…
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…
The min-knapsack problem with compactness constraints extends the classical knapsack problem, in the case of ordered items, by introducing a restriction ensuring that they cannot be too far apart. This problem has applications in…
Motivated by the dynamic assortment offerings and item pricings occurring in e-commerce, we study a general problem of allocating finite inventories to heterogeneous customers arriving sequentially. We analyze this problem under the…
Online allocation problems with resource constraints have a rich history in operations research. In this paper, we introduce the \emph{regularized online allocation problem}, a variant that includes a non-linear regularizer acting on the…