Related papers: Colored Bin Packing
Bin Packing problems have been widely studied because of their broad applications in different domains. Known as a set of NP-hard problems, they have different vari- ations and many heuristics have been proposed for obtaining approximate…
In this paper, a new type of 3D bin packing problem (BPP) is proposed, in which a number of cuboid-shaped items must be put into a bin one by one orthogonally. The objective is to find a way to place these items that can minimize the…
We study the following variant of the classic {\em bin packing} problem. Given a set of items of various sizes, partitioned into groups, find a packing of the items in a minimum number of identical (unit-size) bins, such that no two items…
We study the weighted generalization of the edge coloring problem where the weight of each color class (matching) equals to the weight of its heaviest edge and the goal is to minimize the sum of the colors' weights. We present a…
Best Fit is a well known online algorithm for the bin packing problem, where a collection of one-dimensional items has to be packed into a minimum number of unit-sized bins. In a seminal work, Kenyon [SODA 1996] introduced the (asymptotic)…
List colouring is an NP-complete decision problem even if the total number of colours is three. It is hard even on planar bipartite graphs. We give a polynomial-time algorithm for solving list colouring of permutation graphs with a bounded…
We use the reconfiguration framework to analyze problems that involve the rearrangement of items among groups. In various applications, a group of items could correspond to the files or jobs assigned to a particular machine, and the goal of…
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…
This paper formally proposes a problem about the efficient utilization of the four dimensional space-time. Given a cuboid container, a finite number of rigid cuboid items, and the time length that each item should be continuous baked in the…
We consider the fully dynamic bin packing problem, where items arrive and depart in an online fashion and repacking of previously packed items is allowed. The goal is, of course, to minimize both the number of bins used as well as the…
We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any…
Bin packing is an algorithmic problem that arises in diverse applications such as remnant inventory systems, shipping logistics, and appointment scheduling. In its simplest variant, a sequence of $T$ items (e.g., orders for raw material,…
Many approximation algorithms and heuristic algorithms to find a fair clustering have emerged. In this paper we define a new and natural variant of fair clustering problem and design a polynomial time algorithm to compute an optimal fair…
The list coloring problem is a variation of the classical vertex coloring problem, extensively studied in recent years, where each vertex has a restricted list of allowed colors, and having some variations as the $(\gamma,\mu)$-coloring,…
Given items of different sizes and a fixed bin capacity, the bin-packing problem is to pack these items into the minimum number of bins such that the sum of the item sizes in each bin does not exceed the capacity. We define a new variant,…
Ensuring fairness in computational problems has emerged as a $key$ topic during recent years, buoyed by considerations for equitable resource distributions and social justice. It $is$ possible to incorporate fairness in computational…
In this paper we consider clustering problems in which each point is endowed with a color. The goal is to cluster the points to minimize the classical clustering cost but with the additional constraint that no color is over-represented in…
This paper presents a parallel genetic algorithm for three dimensional bin packing with heterogeneous bins using Hadoop Map-Reduce framework. The most common three dimensional bin packing problem which packs given set of boxes into minimum…
In this paper we formulate the problem of packing unequal rectangles/squares into a fixed size circular container as a mixed-integer nonlinear program. Here we pack rectangles so as to maximise some objective (e.g. maximise the number of…
Consolidation of loose packages into transport units is a fundamental activity offered by logistics service-providers. Moving the transport units instead of loose packages is faster (with one movement only, multiple packages are loaded…