Related papers: Improved approximation bounds for Vector Bin Packi…
Packing problems are in general NP-hard, even for simple cases. Since now there are no highly efficient algorithms available for solving packing problems. The two-dimensional bin packing problem is about packing all given rectangular items,…
In two-dimensional geometric knapsack problem, we are given a set of n axis-aligned rectangular items and an axis-aligned square-shaped knapsack. Each item has integral width, integral height and an associated integral profit. The goal is…
The Restricted Assignment Problem is a prominent special case of Scheduling on Parallel Unrelated Machines. For the strongest known linear programming relaxation, the configuration LP, we improve the non-constructive bound on its…
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…
In this paper, we provide a new scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set defined by finitely many polynomial inequalities. More…
We study black-box vector optimization with Gaussian process bandits, where there is an incomplete order relation on objective vectors described by a polyhedral convex cone. Existing black-box vector optimization approaches either suffer…
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…
Consider the classical Bin Packing problem with $d$ different item sizes $s_i$ and amounts of items $a_i.$ The support of a Bin Packing solution is the number of differently filled bins. In this work, we show that the lower bound on the…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
The Matching Augmentation Problem (MAP) has recently received significant attention as an important step towards better approximation algorithms for finding cheap $2$-edge connected subgraphs. This has culminated in a…
We consider a Two-Bar Charts Packing Problem (2-BCPP), in which it is necessary to pack two-bar charts (2-BCs) in a unit-height strip of minimum length. The problem is a generalization of the Bin Packing Problem (BPP). Earlier, we proposed…
Bin packing problem examines the minimum number of identical bins needed to pack a set of items of various weights. This problem arises in various areas of the artificial intelligence demanding derivation of the exact solutions in the…
New versions and extensions of Benson's outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each…
In this work, we propose an outer approximation algorithm for solving bounded convex vector optimization problems (CVOPs). The scalarization model solved iteratively within the algorithm is a modification of the norm-minimizing…
We revisit the approximate Voronoi cells approach for solving the closest vector problem with preprocessing (CVPP) on high-dimensional lattices, and settle the open problem of Doulgerakis-Laarhoven-De Weger [PQCrypto, 2019] of determining…
First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general…
Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set…
This paper addresses a quadratic problem with assignment constraints, an NP-hard combinatorial optimization problem arisen from facility location, multiple-input multiple-output detection, and maximum mean discrepancy calculation et al. The…
We introduce a new approximate solution technique for first-order Markov decision processes (FOMDPs). Representing the value function linearly w.r.t. a set of first-order basis functions, we compute suitable weights by casting the…
The goal of this paper is to understand how exponential-time approximation algorithms can be obtained from existing polynomial-time approximation algorithms, existing parameterized exact algorithms, and existing parameterized approximation…