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In the online matching on the line problem, the task is to match a set of requests $R$ online to a given set of servers $S$. The distance metric between any two points in $R\,\cup\, S$ is a line metric and the objective for the online…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
In the well-known Minimum Linear Arrangement problem (MinLA), the goal is to arrange the nodes of an undirected graph into a permutation so that the total stretch of the edges is minimized. This paper studies an online (learning) variant of…
The Container Relocation Problem (CRP) is concerned with finding a sequence of moves of containers that minimizes the number of relocations needed to retrieve all containers respecting a given order of retrieval. While the problem is known…
We consider the online problem of packing circles into a square container. A sequence of circles has to be packed one at a time, without knowledge of the following incoming circles and without moving previously packed circles. We present an…
Motivated by applications in the gig economy, we study approximation algorithms for a \emph{sequential pricing problem}. The input is a bipartite graph $G=(I,J,E)$ between individuals $I$ and jobs $J$. The platform has a value of $v_j$ for…
Stochastic matching is the stochastic version of the well-known matching problem, which consists in maximizing the rewards of a matching under a set of probability distributions associated with the nodes and edges. In most stochastic…
The NP-hard maximum value preordering problem is both a joint relaxation and a hybrid of the clique partition problem (a clustering problem) and the partial ordering problem. Toward approximate solutions and lower bounds, we introduce a…
We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
The Bin Packing Problem is one of the most important Combinatorial Optimization problems in optimization and has a lot of real-world applications. Many approximation algorithms have been presented for this problem because of its NP-hard…
In the Priority Steiner Tree (PST) problem, we are given an undirected graph $G=(V,E)$ with a source $s \in V$ and terminals $T \subseteq V \setminus \{s\}$, where each terminal $v \in T$ requires a nonnegative priority $P(v)$. The goal is…
The subset sum algorithm is a natural heuristic for the classical Bin Packing problem: In each iteration, the algorithm finds among the unpacked items, a maximum size set of items that fits into a new bin. More than 35 years after its first…
An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained…
Given an approximation algorithm $A$, we want to find the input with the worst approximation ratio, i.e., the input for which $A$'s output's objective value is the worst possible compared to the optimal solution's objective value. Such hard…
Packing a given sequence of items into as few bins as possible in an online fashion is a widely studied problem. We improve lower bounds for packing boxes into bins in two or more dimensions, both for general algorithms for squares and…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of…
The convex hull cheapest insertion heuristic is a well-known method that efficiently generates good solutions to the Traveling Salesperson Problem. However, this heuristic has not been adapted to account for precedence constraints that…
Set packing is a fundamental problem that generalises some well-known combinatorial optimization problems and knows a lot of applications. It is equivalent to hypergraph matching and it is strongly related to the maximum independent set…
In this work, we study the square min-sum bin packing problem (SMSBPP), where a list of square items has to be packed into indexed square bins of dimensions $1 \times 1$ with no overlap between the areas of the items. The bins are indexed…