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We consider the 0-1 Incremental Knapsack Problem (IKP) where the capacity grows over time periods and if an item is placed in the knapsack in a certain period, it cannot be removed afterwards. The contribution of a packed item in each time…

Data Structures and Algorithms · Computer Science 2018-01-16 Federico Della Croce , Ulrich Pferschy , Rosario Scatamacchia

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Optimization and Control · Mathematics 2016-10-31 Insoon Yang , Samuel A. Burden , Ram Rajagopal , S. Shankar Sastry , Claire J. Tomlin

This paper derives polynomial-time approximation schemes for several NP-hard stochastic optimization problems from the algorithmic mechanism design and operations research literatures. The problems we consider involve a principal or seller…

Computer Science and Game Theory · Computer Science 2025-09-18 Robin Bowers , Marius Garbea , Emmanouil Pountourakis , Samuel Taggart

A class of optimization problems characterized by a weighted finite-sum objective function subject to box constraints is considered. We propose a novel stochastic optimization method, named AS-BOX (\text{A}ddi\-ti\-onal \text{S}ampling for…

Optimization and Control · Mathematics 2025-11-26 Nataša Krejić , Nataša Krklec Jerinkić , Tijana Ostojić , Nemanja Vučićević

We study the two-dimensional geometric knapsack problem (2DK) in which we are given a set of n axis-aligned rectangular items, each one with an associated profit, and an axis-aligned square knapsack. The goal is to find a (non-overlapping)…

Data Structures and Algorithms · Computer Science 2017-11-22 Waldo Gálvez , Fabrizio Grandoni , Sandy Heydrich , Salvatore Ingala , Arindam Khan , Andreas Wiese

This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…

Data Structures and Algorithms · Computer Science 2026-02-12 Kobe Grobben , Phablo F. S. Moura , Hande Yaman

We give the first polynomial-time approximation schemes (PTASs) for the following problems: (1) uniform facility location in edge-weighted planar graphs; (2) $k$-median and $k$-means in edge-weighted planar graphs; (3) $k$-means in…

Data Structures and Algorithms · Computer Science 2016-04-08 Vincent Cohen-Addad , Philip N. Klein , Claire Mathieu

In real-time systems, in addition to the functional correctness recurrent tasks must fulfill timing constraints to ensure the correct behavior of the system. Partitioned scheduling is widely used in real-time systems, i.e., the tasks are…

Data Structures and Algorithms · Computer Science 2018-09-13 Jian-Jia Chen , Nikhil Bansal , Samarjit Chakraborty , Georg von der Brüggen

We revisit the classic online bin packing problem. In this problem, items of positive sizes no larger than 1 are presented one by one to be packed into subsets called "bins" of total sizes no larger than 1, such that every item is assigned…

Data Structures and Algorithms · Computer Science 2017-07-07 János Balogh , József Békési , György Dósa , Leah Epstein , Asaf Levin

We present a general technique for approximating bicriteria minimization problems with positive-valued, polynomially computable objective functions. Given $0<\epsilon\leq1$ and a polynomial-time $\alpha$-approximation algorithm for the…

Optimization and Control · Mathematics 2017-11-16 Pascal Halffmann , Stefan Ruzika , Clemens Thielen , David Willems

We propose a Fully Polynomial-Time Approximation Scheme (FPTAS) for stochastic dynamic programs with multidimensional action, scalar state, convex costs and linear state transition function. The action spaces are polyhedral and described by…

Discrete Mathematics · Computer Science 2020-06-11 Nir Halman , Giacomo Nannicini

Motivated by a transit line planning problem in transportation systems, we investigate the following capacitated assignment problem under a budget constraint. Our model involves $L$ bins and $P$ items. Each bin $l$ has a utilization cost…

Optimization and Control · Mathematics 2024-10-11 Hongyi Jiang , Samitha Samaranayake

A multiple knapsack constraint over a set of items is defined by a set of bins of arbitrary capacities, and a weight for each of the items. An assignment for the constraint is an allocation of subsets of items to the bins which adheres to…

Data Structures and Algorithms · Computer Science 2021-06-29 Yaron Fairstein , Ariel Kulik , Hadas Shachnai

We study several stochastic combinatorial problems, including the expected utility maximization problem, the stochastic knapsack problem and the stochastic bin packing problem. A common technical challenge in these problems is to optimize…

Data Structures and Algorithms · Computer Science 2013-03-20 Jian Li , Wen Yuan

Motivated by modern-day applications such as Attended Home Delivery and Preference-based Group Scheduling, where decision makers wish to steer a large number of customers toward choosing the exact same alternative, we introduce a novel…

Optimization and Control · Mathematics 2025-02-13 Omar El Housni , Marouane Ibn Brahim , Danny Segev

In this paper, we study the {\em green bin packing} (GBP) problem where $\beta \ge 0$ and $G \in [0, 1]$ are two given values as part of the input. The energy consumed by a bin is $\max \{0, \beta (x-G) \}$ where $x$ is the total size of…

Data Structures and Algorithms · Computer Science 2026-02-20 Mingyang Gong , Brendan Mumey

Packing cost accounts for a large part of the e-commerce logistics cost. Mining the patterns of customer orders and designing suitable packing bins help to reduce operating cost. In the classical bin packing problem, a given set of…

Data Structures and Algorithms · Computer Science 2018-12-10 Xinhang Zhang , Haoyuan Hu , Longfei Wang , Zhijun Sun , Ying Zhang , Kunpeng Han , Yinghui Xu

We present the first polynomial-time approximation schemes (PTASes) for the following subset-connectivity problems in edge-weighted graphs of bounded genus: Steiner tree, low-connectivity survivable-network design, and subset TSP. The…

Discrete Mathematics · Computer Science 2011-03-02 Glencora Borradaile , Erik D. Demaine , Siamak Tazari

Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in…

Artificial Intelligence · Computer Science 2011-10-12 A. S. Fukunaga , R. E. Korf

We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual…

Data Structures and Algorithms · Computer Science 2015-06-02 Christos Koufogiannakis , Neal E. Young