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We consider the classic problem of scheduling jobs with precedence constraints on identical machines to minimize makespan, in the presence of communication delays. In this setting, denoted by $\mathsf{P} \mid \mathsf{prec}, c \mid…
The non-clairvoyant scheduling problem has gained new interest within learning-augmented algorithms, where the decision-maker is equipped with predictions without any quality guarantees. In practical settings, access to predictions may be…
Equivariant neural networks have shown great success in reinforcement learning, improving sample efficiency and generalization when there is symmetry in the task. However, in many problems, only approximate symmetry is present, which makes…
In this work we revisit the elementary scheduling problem $1||\sum p_j U_j$. The goal is to select, among $n$ jobs with processing times and due dates, a subset of jobs with maximum total processing time that can be scheduled in sequence…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
In the field of constraint satisfaction problems (CSP), promise CSPs are an exciting new direction of study. In a promise CSP, each constraint comes in two forms: "strict" and "weak," and in the associated decision problem one must…
We present an algorithm for approximating semidefinite programs with running time that is sublinear in the number of entries in the semidefinite instance. We also present lower bounds that show our algorithm to have a nearly optimal running…
In this paper, we identify partial correlation information structures that allow for simpler reformulations in evaluating the maximum expected value of mixed integer linear programs with random objective coefficients. To this end, assuming…
We present an alternate formulation of the partial assignment problem as matching random clique complexes, that are higher-order analogues of random graphs, designed to provide a set of invariants that better detect higher-order structure.…
We revisit the deadline version of the discrete time-cost tradeoff problem for the special case of bounded depth. Such instances occur for example in VLSI design. The depth of an instance is the number of jobs in a longest chain and is…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
Quadratic assignment problems are a fundamental class of combinatorial optimization problems which are ubiquitous in applications, yet their exact resolution is NP-hard. To circumvent this impasse, it was proposed to regularize such…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
We study the early work scheduling problem on identical parallel machines in order to maximize the total early work, i.e., the parts of non-preemptive jobs executed before a common due date. By preprocessing and constructing an auxiliary…
We consider a type of optimal switching problems with non-uniform execution delays and ramping. Such problems frequently occur in the operation of economical and engineering systems. We first provide a solution to the problem by applying a…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
We consider the classic problem of scheduling jobs on unrelated machines so as to minimize the weighted sum of completion times. Recently, for a small constant $\varepsilon >0 $, Bansal et al. gave a $(3/2-\varepsilon)$-approximation…
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…
Fixed-parameter algorithms, approximation algorithms and moderately exponential algorithms are three major approaches to algorithms design. While each of them being very active in its own, there is an increasing attention to the connection…
We study the incremental knapsack problem, where one wishes to sequentially pack items into a knapsack whose capacity expands over a finite planning horizon, with the objective of maximizing time-averaged profits. While various…