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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…
While rectangular and box-shaped objects dominate the classic discourse of theoretic investigations, a fascinating frontier lies in packing more complex shapes. Given recent insights that convex polygons do not allow for constant…
Online Contention Resolution Schemes (OCRS's) represent a modern tool for selecting a subset of elements, subject to resource constraints, when the elements are presented to the algorithm sequentially. OCRS's have led to some of the…
We consider a special case of the generalized minimum spanning tree problem (GMST) and the generalized travelling salesman problem (GTSP) where we are given a set of points inside the integer grid (in Euclidean plane) where each grid cell…
In the random-order online set cover problem, the instance with $m$ sets and $n$ elements is chosen in a worst-case fashion, but then the elements arrive in a uniformly random order. Can this random-order model allow us to circumvent the…
For many online problems, it is known that the uniform arrival order enables the design of algorithms with much better performance guarantees than under worst-case. The quintessential example is the secretary problem. If the sequence of…
In the secretary problem we are faced with an online sequence of elements with values. Upon seeing an element we have to make an irrevocable take-it-or-leave-it decision. The goal is to maximize the probability of picking the element of…
In many problems, the inputs arrive over time, and must be dealt with irrevocably when they arrive. Such problems are online problems. A common method of solving online problems is to first solve the corresponding linear program, and then…
Many problems on data streams have been studied at two extremes of difficulty: either allowing randomized algorithms, in the static setting (where they should err with bounded probability on the worst case stream); or when only…
A fundamental problem in distributed computing is the distribution of requests to a set of uniform servers without a centralized controller. Classically, such problems are modeled as static balls into bins processes, where $m$ balls (tasks)…
In the streaming model, the order of the stream can significantly affect the difficulty of a problem. A $t$-semirandom stream was introduced as an interpolation between random-order ($t=1$) and adversarial-order ($t=n$) streams where an…
We consider the online resource minimization problem in which jobs with hard deadlines arrive online over time at their release dates. The task is to determine a feasible schedule on a minimum number of machines. We rigorously study this…
We present sorting algorithms that represent the fastest known techniques for a wide range of input sizes, input distributions, data types, and machines. A part of the speed advantage is due to the feature to work in-place. Previously, the…
This paper studies Makespan Minimization in the secretary model. Formally, jobs, specified by their processing times, are presented in a uniformly random order. An online algorithm has to assign each job permanently and irrevocably to one…
We study the online traveling repairperson problem on a line within the recently proposed learning-augmented framework, which provides predictions on the requests to be served via machine learning. In the original model (with no…
A new characterization of Hamiltonian graphs using f-cutset matrix is proposed. Based on this new characterization, a new exact polynomial time algorithm for the traveling salesman problem (TSP) is developed. We then define the so-called…
In this paper, we investigate the online parcel assignment (OPA) problem, in which each stochastically generated parcel needs to be assigned to a candidate route for delivery to minimize the total cost subject to certain business…
Express companies are deploying more robotic sorting systems, where mobile robots are used to sort incoming parcels by destination. In this study, we propose an integrated assignment and path-finding method for robots in such sorting…
Strategic product placement can have a strong influence on customer purchase behavior in physical stores as well as online platforms. Motivated by this, we consider the problem of optimizing the placement of substitutable products in…
In this paper, we investigate the online allocation problem of maximizing the overall revenue subject to both lower and upper bound constraints. Compared to the extensively studied online problems with only resource upper bounds, the…