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Parallel machine scheduling has been extensively studied in the past decades, with applications ranging from production planning to job processing in large computing clusters. In this work we study some of these fundamental optimization…
In this paper we study paramertized motion planning algorithms which provide universal and flexible solutions to diverse motion planning problems. Such algorithms are intended to function under a variety of external conditions which are…
In this paper we study a resource allocation problem that encodes correlation between items in terms of \conflict and maximizes the minimum utility of the agents under a conflict free allocation. Admittedly, the problem is computationally…
In certain real-world optimization scenarios, practitioners are not interested in solving multiple problems but rather in finding the best solution to a single, specific problem. When the computational budget is large relative to the cost…
This paper proposes an optimal allocation problem with ramified transport technology in a spatial economy. Ramified transportation is used to model the transport economy of scale in group transportation observed widely in both nature and…
Autonomous robots are increasingly utilized in realistic scenarios with multiple complex tasks. In these scenarios, there may be a preferred way of completing all of the given tasks, but it is often in conflict with optimal execution.…
In many applications such as rationing medical care and supplies, university admissions, and the assignment of public housing, the decision of who receives an allocation can be justified by various normative criteria. Such settings have…
This work studies rearrangement problems involving the sorting of robots or objects in stack-like containers, which can be accessed only from one side. Two scenarios are considered: one where every robot or object needs to reach a…
Quadratic assignment problem is one of the great challenges in combinatorial optimization. It has many applications in Operations research and Computer Science. In this paper, the author extends the most-used rounding approach to a…
In this paper we consider multiple constrained resource allocation problems, where the constraints can be specified by formulating activity dependency restrictions or by using game-theoretic models. All the problems are focused on generic…
In this paper, we present novel randomized algorithms for solving saddle point problems whose dual feasible region is given by the direct product of many convex sets. Our algorithms can achieve an ${\cal O}(1/N)$ and ${\cal O}(1/N^2)$ rate…
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…
Stable matching is a fundamental area with many practical applications, such as centralised clearinghouses for school choice or job markets. Recent work has introduced the paradigm of near-feasibility in capacitated matching settings, where…
Optimization is a key task in a number of applications. When the set of feasible solutions under consideration is of combinatorial nature and described in an implicit way as a set of constraints, optimization is typically NP-hard.…
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
We introduce a novel family of mechanisms for constrained allocation problems which we call local priority mechanisms. These mechanisms are parameterized by a function which assigns a set of agents, the local compromisers, to every…
Pareto-optimality plays a central role in evaluating the efficiency of solutions to allocation problems, such as house allocation, school choice, and kidney exchange. We introduce a general linear programming problem subject to…
We introduce and study a multi-class online resource allocation problem with group fairness guarantees. The problem involves allocating a fixed amount of resources to a sequence of agents, each belonging to a specific group. The primary…
We discuss the computational complexity and feasibility properties of scenario based techniques for uncertain optimization programs. We consider different solution alternatives ranging from the standard scenario approach to recursive…
Path planning is typically considered in Artificial Intelligence as a graph searching problem and R* is state-of-the-art algorithm tailored to solve it. The algorithm decomposes given path finding task into the series of subtasks each of…