Related papers: Improved Analysis of two Algorithms for Min-Weight…
We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint…
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…
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…
In this paper I investigate several offline and online data transfer scheduling problems and propose efficient algorithms and techniques for addressing them. In the offline case, I present a novel, heuristic, algorithm for scheduling files…
We consider several combinatorial optimization problems which combine the classic shop scheduling problems, namely open shop scheduling or job shop scheduling, and the shortest path problem. The objective of the obtained problem is to…
The set of 2-dimensional packing problems builds an important class of optimization problems and Strip Packing together with 2-dimensional Bin Packing and 2-dimensional Knapsack is one of the most famous of these problems. Given a set of…
Packing and vehicle routing problems play an important role in the area of supply chain management. In this paper, we introduce a non-linear knapsack problem that occurs when packing items along a fixed route and taking into account travel…
We consider a known variant of bin packing called {\it cardinality constrained bin packing}, also called {\it bin packing with cardinality constraints} (BPCC). In this problem, there is a parameter k\geq 2, and items of rational sizes in…
The \Problem{knapsack} problem is a fundamental problem in combinatorial optimization. It has been studied extensively from theoretical as well as practical perspectives as it is one of the most well-known NP-hard problems. The goal is to…
We present a packing-based approximation algorithm for the $k$-Set Cover problem. We introduce a new local search-based $k$-set packing heuristic, and call it Restricted $k$-Set Packing. We analyze its tight approximation ratio via a…
Given an edge-weighted (metric/general) complete graph with $n$ vertices, the maximum weight (metric/general) $k$-cycle/path packing problem is to find a set of $\frac{n}{k}$ vertex-disjoint $k$-cycles/paths such that the total weight is…
Two-Bar Charts Packing Problem is to pack $n$ two-bar charts (2-BCs) in a minimal number of unit-capacity bins. This problem generalizes the strongly NP-hard Bin Packing Problem. We prove that the problem remains strongly NP-hard even if…
The bin covering problem asks for covering a maximum number of bins with an online sequence of $n$ items of different sizes in the range $(0,1]$; a bin is said to be covered if it receives items of total size at least 1. We study this…
The online knapsack problem is a classic problem in the field of online algorithms. Its canonical version asks how to pack items of different values and weights arriving online into a capacity-limited knapsack so as to maximize the total…
Imagine yourself moving to another place, and therefore, you need to pack all of your belongings into moving boxes with some capacity. In the classical bin packing model, you would try to minimize the number of boxes, knowing the exact size…
Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances,…
We investigate pseudopolynomial-time algorithms for Bounded Knapsack and Bounded Subset Sum. Recent years have seen a growing interest in settling their fine-grained complexity with respect to various parameters. For Bounded Knapsack, the…
We give a deterministic, polynomial-time algorithm for approximately counting the number of {0,1}-solutions to any instance of the knapsack problem. On an instance of length n with total weight W and accuracy parameter eps, our algorithm…
The Bin Packing Problem is a classic problem with wide industrial applicability. In fact, the efficient packing of items into bins is one of the toughest challenges in many logistic corporations and is a critical issue for reducing storage…
Following the work of Anily et al., we consider a variant of bin packing, called "bin packing with general cost structures" (GCBP) and design an asymptotic fully polynomial time approximation scheme (AFPTAS) for this problem. In the classic…