Related papers: Complexity Results and Approximation Strategies fo…
Quadratic assignment problems are a fundamental class of combinatorial optimization problems which are ubiquitous in applications, yet their exact resolution is NP-hard. To circumvent this impasse, it was proposed to regularize such…
The Multidimensional Assignment Problem (MAP or s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s have also a number of…
Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…
In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We initiate the study of approximation algorithms and computational barriers for constructing sparse $\alpha$-navigable graphs [IX23, DGM+24], a core primitive underlying recent advances in graph-based nearest neighbor search. Given an…
We investigate sparse matrix bipartitioning -- a problem where we minimize the communication volume in parallel sparse matrix-vector multiplication. We prove, by reduction from graph bisection, that this problem is $\mathcal{NP}$-complete…
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
Many Bayesian network modelling applications suffer from the issue of data scarcity. Hence the use of expert judgement often becomes necessary to determine the parameters of the conditional probability tables (CPTs) throughout the network.…
We study classic scheduling problems on uniformly related machines. Efficient polynomial time approximation schemes (EPTAS's) are fast and practical approximation schemes. New methods and techniques are essential in developing such improved…
We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…
When belief propagation (BP) converges, it does so to a stationary point of the Bethe free energy $F$, and is often strikingly accurate. However, it may converge only to a local optimum or may not converge at all. An algorithm was recently…
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,…
The Capacitated Vehicle Routing Problem (CVRP) is a core NP-hard problem in the field of combinatorial optimization. It aims to plan optimal routes for a fleet of vehicles with uniform capacity, serving a set of customers with specific…
The authors give an approximation method for Bayesian inference in arena model, which is focused on paired comparisons with eliminations and bifurcations. The approximation method simplifies the inference by reducing parameters and…
The maximum a-posteriori (MAP) perturbation framework has emerged as a useful approach for inference and learning in high dimensional complex models. By maximizing a randomly perturbed potential function, MAP perturbations generate unbiased…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
Multi-agent path planning is a challenging problem with numerous real-life applications. Running a centralized search such as A* in the combined state space of all units is complete and cost-optimal, but scales poorly, as the state space…
Structure and parameters in a Bayesian network uniquely specify the probability distribution of the modeled domain. The locality of both structure and probabilistic information are the great benefits of Bayesian networks and require the…
A major inference task in Bayesian networks is explaining why some variables are observed in their particular states using a set of target variables. Existing methods for solving this problem often generate explanations that are either too…