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Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
We introduce and study $\ell_p$-norm-multiway-cut: the input here is an undirected graph with non-negative edge weights along with $k$ terminals and the goal is to find a partition of the vertex set into $k$ parts each containing exactly…
In this paper, we present an exact algorithm for optimizing two linear fractional over the efficient set of a multi-objective integer quadratic problem. This type of problems arises when two decision-makers, such as firms, each have a…
Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation in processing graphs. Recently, size, variety, and structural complexity of these networks has grown dramatically.…
The input to the Multiway Cut problem is a weighted undirected graph, with nonnegative edge weights, and $k$ designated terminals. The goal is to partition the vertices of the graph into $k$ parts, each containing exactly one of the…
We present a novel framework for dynamic cut aggregation in L-shaped algorithms. The aim is to improve the parallel performance of distributed L-shaped algorithms through reduced communication latency and load imbalance. We show how…
In this paper, we study the problem of optimal multi-robot path planning (MPP) on graphs. We propose two multiflow based integer linear programming (ILP) models that computes minimum last arrival time and minimum total distance solutions…
We propose a new algorithm for solving multistage stochastic mixed integer linear programming (MILP) problems with complete continuous recourse. In a similar way to cutting plane methods, we construct nonlinear Lipschitz cuts to build lower…
Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
Mixed Integer Linear Programming (MILP) is a pillar of mathematical optimization that offers a powerful modeling language for a wide range of applications. During the past decades, enormous algorithmic progress has been made in solving…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
Lineage tracing, the joint segmentation and tracking of living cells as they move and divide in a sequence of light microscopy images, is a challenging task. Jug et al. have proposed a mathematical abstraction of this task, the moral…
The Simplex tableau has been broadly used and investigated in the industry and academia. With the advent of the big data era, ever larger problems are posed to be solved in ever larger machines whose architecture type did not exist in the…
Finding min $s$-$t$ cuts in graphs is a basic algorithmic tool with applications in image segmentation, community detection, reinforcement learning, and data clustering. In this problem, we are given two nodes as terminals, and the goal is…
We developed a flexible parallel algorithm for graph summarization based on vertex-centric programming and parameterized message passing. The base algorithm supports infinitely many structural graph summary models defined in a formal…
The distributed operating room (OR) scheduling problem aims to find an assignment of surgeries to ORs across collaborating hospitals that share their waiting lists and ORs. We propose a stochastic extension of this problem where surgery…
In this paper, we present an advanced analysis of near optimal algorithms that use limited space to solve the frequency estimation, heavy hitters, frequent items, and top-k approximation in the bounded deletion model. We define the family…
We develop a novel distributed algorithm for the minimum cut problem. We primarily aim at solving large sparse problems. Assuming vertices of the graph are partitioned into several regions, the algorithm performs path augmentations inside…
When approaching to problems in computer science, we often encounter situations where a subset of a finite set maximizing some utility function needs to be selected. Some of such utility functions are known to be approximately submodular.…