相关论文: Linear Programming helps solving large multi-unit …

This paper presents an evaluation framework for assessing Large Language Models' (LLMs) capabilities in combinatorial optimization, specifically addressing the 2D bin-packing problem. We introduce a systematic methodology that combines LLMs…

This paper investigates the integration of large language models (LLMs) as reasoning agents in repeated spectrum auctions within heterogeneous networks (HetNets). While auction-based mechanisms have been widely employed for efficient…

The current art in optimal combinatorial auctions is limited to handling the case of single units of multiple items, with each bidder bidding on exactly one bundle (single minded bidders). This paper extends the current art by proposing an…

Register allocation (mapping variables to processor registers or memory) and instruction scheduling (reordering instructions to increase instruction-level parallelism) are essential tasks for generating efficient assembly code in a…

Mixed Integer Linear Programming (MILP) is a pillar of mathematical optimization that offers a powerful modeling language for a wide range of applications. During the past decades, enormous algorithmic progress has been made in solving…

Two general algorithms based on opportunity costs are given for approximating a revenue-maximizing set of bids an auctioneer should accept, in a combinatorial auction in which each bidder offers a price for some subset of the available…

This paper introduces a combinatorial optimization approach to register allocation and instruction scheduling, two central compiler problems. Combinatorial optimization has the potential to solve these problems optimally and to exploit…

The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…

Auction has been used to allocate resources or tasks to processes, machines or other autonomous entities in distributed systems. When different bidders have different demands and valuations on different types of resources or tasks, the…

Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are…

This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…

Budgets play a significant role in real-world sequential auction markets such as those implemented by internet companies. To maximize the value provided to auction participants, spending is smoothed across auctions so budgets are used for…

We consider repeated multi-unit auctions with uniform pricing, which are widely used in practice for allocating goods such as carbon licenses. In each round, $K$ identical units of a good are sold to a group of buyers that have valuations…

Recent advances in machine learning have spurred significant interest in learning-augmented algorithms, particularly for online optimization. A growing body of work has studied online bidding in this framework, aiming to characterize the…

We study the Maximum Budgeted Allocation problem, i.e., the problem of selling a set of $m$ indivisible goods to $n$ players, each with a separate budget, such that we maximize the collected revenue. Since the natural assignment LP is known…

We consider the problem of controlling a fully specified Markov decision process (MDP), also known as the planning problem, when the state space is very large and calculating the optimal policy is intractable. Instead, we pursue the more…

Auctions are widely used in exchanges to match buy and sell requests. Once the buyers and sellers place their requests, the exchange determines how these requests are to be matched. The two most popular objectives used while determining the…

Auctions are important mechanisms extensively implemented in various markets, e.g., search engines' keyword auctions, antique auctions, etc. Finding an optimal auction mechanism is extremely difficult due to the constraints of imperfect…

A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…

This paper presents a novel, high-performance, graphical processing unit-based algorithm for efficiently solving two-dimensional linear programs in batches. The domain of two-dimensional linear programs is particularly useful due to the…