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We study the approximability of two related machine scheduling problems. In the late work minimization problem, there are identical parallel machines and the jobs have a common due date. The objective is to minimize the late work, defined…
Many problems are NP-hard and, unless P = NP, do not admit polynomial-time exact algorithms. The fastest known exact algorithms exactly usually take time exponential in the input size. Much research effort has gone into obtaining faster…
Advance reservation is important to guarantee the quality of services of jobs by allowing exclusive access to resources over a defined time interval on resources. It is a challenge for the scheduler to organize available resources…
A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound andcomplete characterization of the set of polynomial time computable functions is obtained. As a consequence,…
In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…
This paper introduces bucket calculus, a novel mathematical framework that fundamentally transforms the computational complexity landscape of parallel machine scheduling optimization. We address the strongly NP-hard problem…
The question of knowing whether the policy Iteration algorithm (PI) for solving Markov Decision Processes (MDPs) has exponential or (strongly) polynomial complexity has attracted much attention in the last 50 years. Recently, Fearnley…
Recently, the problem of multitasking scheduling has attracted a lot of attention in the service industries where workers frequently perform multiple tasks by switching from one task to another. Hall, Leung and Li (Discrete Applied…
Owing to data-intensive large-scale applications, distributed computation systems have gained significant recent interest, due to their ability of running such tasks over a large number of commodity nodes in a time efficient manner. One of…
Message passing type algorithms such as the so-called Belief Propagation algorithm have recently gained a lot of attention in the statistics, signal processing and machine learning communities as attractive algorithms for solving a variety…
We study the problem of minimizing a multivariate polynomial function over the unit hypercube. By representing the polynomial through a hypergraph and exploiting its sparsity structure, we establish a new sufficient condition under which…
In the classic Integer Programming (IP) problem, the objective is to decide whether, for a given $m \times n$ matrix $A$ and an $m$-vector $b=(b_1,\dots, b_m)$, there is a non-negative integer $n$-vector $x$ such that $Ax=b$. Solving (IP)…
Given a database, the private information retrieval (PIR) protocol allows a user to make queries to several servers and retrieve a certain item of the database via the feedbacks, without revealing the privacy of the specific item to any…
Propagation of linear constraints has become a crucial sub-routine in modern Mixed-Integer Programming (MIP) solvers. In practice, iterative algorithms with tolerance-based stopping criteria are used to avoid problems with slow or infinite…
The network-based study of financial systems has received considerable attention in recent years but has seldom explicitly incorporated the dynamic aspects of such systems. We consider this problem setting from the temporal point of view…
Binary (0-1) integer programming (BIP) is pivotal in scientific domains requiring discrete decision-making. As the advance of AI computing, recent works explore neural network-based solvers for integer linear programming (ILP) problems.…
One of the primary sources of unpredictability in modern multi-core embedded systems is contention over shared memory resources, such as caches, interconnects, and DRAM. Despite significant achievements in the design and analysis of…
Exact queueing analysis of erasure networks with network coding in a finite buffer regime is an extremely hard problem due to the large number of states in the network. In such networks, packets are lost due to either link erasures or due…
In scenarios that require teamwork, we usually have at hand a variety of specific tasks, for which we need to form a team in order to carry out each one. Here we target the problem of matching teams with tasks within the context of…
In the problem called single resource constraint scheduling, we are given $m$ identical machines and a set of jobs, each needing one machine to be processed as well as a share of a limited renewable resource $R$. A schedule of these jobs is…