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We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…
We give polynomial-time approximation schemes for monotone maximization problems expressible in terms of distances (up to a fixed upper bound) and efficiently solvable in graphs of bounded treewidth. These schemes apply in all fractionally…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
Object triangulation, 3-D object tracking, feature correspondence, and camera calibration are key problems for estimation from camera networks. This paper addresses these problems within a unified Bayesian framework for joint multi-object…
We propose two minimal solutions to the problem of relative pose estimation of (i) a calibrated camera from four points in two views and (ii) a calibrated generalized camera from five points in two views. In both cases, the relative…
In this paper we study the task of approach of two mobile agents having the same limited range of vision and moving asynchronously in the plane. This task consists in getting them in finite time within each other's range of vision. The…
In this work we present a unified method of relative camera pose estimation from points and lines correspondences. Given a set of 2D points and lines correspondences in three views, of which two are known, a method has been developed for…
This paper proposes a fast and online method for jointly performing 3D multi-object tracking and pose estimation using multiple monocular cameras. Our algorithm requires only 2D bounding box and pose detections, eliminating the need for…
We study the challenging problem of estimating the relative pose of three calibrated cameras from four point correspondences. We propose novel efficient solutions to this problem that are based on the simple idea of using four…
Consider a set $P$ of $n$ points in $\mathbb{R}^d$. In the discrete median line segment problem, the objective is to find a line segment bounded by a pair of points in $P$ such that the sum of the Euclidean distances from $P$ to the line…
We study the early work scheduling problem on identical parallel machines in order to maximize the total early work, i.e., the parts of non-preemptive jobs executed before a common due date. By preprocessing and constructing an auxiliary…
With the popularity of drone technologies, aerial photography has become prevalent in many daily scenarios such as environment monitoring, structure inspection, law enforcement etc. A central challenge in this domain is the efficient…
We consider the Subset Sum Ratio Problem ($SSR$), in which given a set of integers the goal is to find two subsets such that the ratio of their sums is as close to~1 as possible, and introduce a family of variations that capture additional…
Recently, the problem of multitasking scheduling has attracted a lot of attention in the service industries where workers frequently perform multiple tasks by switching from one task to another. Hall, Leung and Li (Discrete Applied…
This paper proposes CAMOT, a simple camera angle estimator for multi-object tracking to tackle two problems: 1) occlusion and 2) inaccurate distance estimation in the depth direction. Under the assumption that multiple objects are located…
We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions…
We study the problem of assigning non-overlapping geometric objects centered at a given set of points such that the sum of area covered by them is maximized. If the points are placed on a straight-line and the objects are disks, then the…
Quadrotors are among the most agile flying robots. However, planning time-optimal trajectories at the actuation limit through multiple waypoints remains an open problem. This is crucial for applications such as inspection, delivery, search…
We study polynomial-time approximation algorithms for the Quantum Max-Cut (QMC) problem. Given an edge-weighted graph $G$ on n vertices, the QMC problem is to determine the largest eigenvalue of a particular $2^n \times 2^n$ matrix that…
We study the problem of approximate ranking from observations of pairwise interactions. The goal is to estimate the underlying ranks of $n$ objects from data through interactions of comparison or collaboration. Under a general framework of…