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Bin Packing with Minimum Color Fragmentation (BPMCF) is an extension of the Bin Packing Problem in which each item has a size and a color and the goal is to minimize the sum of the number of bins containing items of each color. In this…
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…
Since the Bin Packing Problem (BPP) is one of the main NP-hard problems, a lot of approximation algorithms have been suggested for it. It has been proven that the best algorithm for BPP has the approximation ratio of 3/2 and the time order…
The goal of this paper is to understand how exponential-time approximation algorithms can be obtained from existing polynomial-time approximation algorithms, existing parameterized exact algorithms, and existing parameterized approximation…
We present a unified framework for designing and analyzing algorithms for online budgeted allocation problems (including online matching) and their generalization, the Online Generalized Assignment Problem (OnGAP). These problems have been…
We consider the approximability of center-based clustering problems where the points to be clustered lie in a metric space, and no candidate centers are specified. We call such problems "continuous", to distinguish from "discrete"…
Recently, Renault (2016) studied the dual bin packing problem in the per-request advice model of online algorithms. He showed that given $O(1/\epsilon)$ advice bits for each input item allows approximating the dual bin packing problem…
The Geometric Bin Packing (GBP) problem is a generalization of Bin Packing where the input is a set of $d$-dimensional rectangles, and the goal is to pack them into unit $d$-dimensional cubes efficiently. It is NP-Hard to obtain a PTAS for…
We study packing LPs in an online model where the columns are presented to the algorithm in random order. This natural problem was investigated in various recent studies motivated, e.g., by online ad allocations and yield management where…
MapReduce has become the de facto standard model for designing distributed algorithms to process big data on a cluster. There has been considerable research on designing efficient MapReduce algorithms for clustering, graph optimization, and…
We consider an assortment optimization problem where a customer chooses a single item from a sequence of sets shown to her, while limited inventories constrain the items offered to customers over time. In the special case where all of the…
Coded multicasting has been shown to improve the caching performance of content delivery networks with multiple caches downstream of a common multicast link. However, the schemes that have been shown to achieve order-optimal perfor- mance…
We study the online unweighted bipartite matching problem in the random arrival order model, with $n$ offline and $n$ online vertices, in the learning-augmented setting: The algorithm is provided with untrusted predictions of the types…
In many online learning problems we are interested in predicting local information about some universe of items. For example, we may want to know whether two items are in the same cluster rather than computing an assignment of items to…
In the Bin Packing problem one is given $n$ items with weights $w_1,\ldots,w_n$ and $m$ bins with capacities $c_1,\ldots,c_m$. The goal is to find a partition of the items into sets $S_1,\ldots,S_m$ such that $w(S_j) \leq c_j$ for every bin…
We study the online clustering problem where data items arrive in an online fashion. The algorithm maintains a clustering of data items into similarity classes. Upon arrival of v, the relation between v and previously arrived items is…
We consider the problem of online allocation (matching, budgeted allocations, and assortments) of reusable resources where an adversarial sequence of resource requests is revealed over time and any allocated resource is used/rented for a…
We study the 2-dimensional vector packing problem, which is a generalization of the classical bin packing problem where each item has 2 distinct weights and each bin has 2 corresponding capacities. The goal is to group items into minimum…
Online bin stretching is an online packing problem where some of the best known lower and upper bounds were found through computational searches. The limiting factor in obtaining better bounds with such methods is the computational time…
Motivated by Internet targeted advertising, we address several ad allocation problems. Prior work has established these problems admit no randomized online algorithm better than $(1-\frac{1}{e})$-competitive…