Related papers: Computing Planar Convex Hulls with a Promise
We consider the problem of counting straight-edge triangulations of a given set $P$ of $n$ points in the plane. Until very recently it was not known whether the exact number of triangulations of $P$ can be computed asymptotically faster…
We prove that, given a closure function the smallest preimage of a closed set can be calculated in polynomial time in the number of closed sets. This confirms a conjecture of Albenque and Knauer and implies that there is a polynomial time…
This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices $\text{SO}(n)$. Such problems are nonconvex due to the constraint $X \in \text{SO}(n)$. Nonetheless, we show…
Traditional algorithms for stochastic optimization require projecting the solution at each iteration into a given domain to ensure its feasibility. When facing complex domains, such as positive semi-definite cones, the projection operation…
Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints…
We study a Faulty Congested Clique model, in which an adversary may fail nodes in the network throughout the computation. We show that any task of $O(n\log{n})$-bit input per node can be solved in roughly $n$ rounds, where $n$ is the size…
This paper considers online convex optimization over a complicated constraint set, which typically consists of multiple functional constraints and a set constraint. The conventional online projection algorithm (Zinkevich, 2003) can be…
A new algorithm for regret minimization in online convex optimization is described. The regret of the algorithm after $T$ time periods is $O(\sqrt{T \log T})$ - which is the minimum possible up to a logarithmic term. In addition, the new…
Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…
We prove that no deterministic output-sensitive algorithm for the planar convex hull and maxima problems can obtain both optimal time and I/O complexity, where the optimality is defined with respect to both the input and output sizes. This…
In this paper, we study the problem of computing a minimum-width axis-aligned cubic shell that encloses a given set of $n$ points in a three-dimensional space. A cubic shell is a closed volume between two concentric and face-parallel cubes.…
The dynamic shortest paths problem on planar graphs asks us to preprocess a planar graph $G$ such that we may support insertions and deletions of edges in $G$ as well as distance queries between any two nodes $u,v$ subject to the constraint…
Recently increasing penetration of renewable energy generation brings challenges for power system operators to perform efficient power generation daily scheduling, due to the intermittent nature of the renewable generation and discrete…
Let $P$ be a $k$-colored set of $n$ points in the plane, $4 \leq k \leq n$. We study the problem of deciding if $P$ contains a subset of four points of different colors such that its Rectilinear Convex Hull has positive area. We show this…
Motivated by the increasing interest in applications of graph geodesic convexity in machine learning and data mining, we present a heuristic for computing the geodesic convex hull of node sets in networks. It generates a set of almost…
Measuring the performance of a classifier is a vital task in machine learning. The running time of an algorithm that computes the measure plays a very small role in an offline setting, for example, when the classifier is being developed by…
Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…
We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…
We consider the {\em Shaped Partition Problem} of partitioning $n$ given vectors in real $k$-space into $p$ parts so as to maximize an arbitrary objective function which is convex on the sum of vectors in each part, subject to arbitrary…
Allen's interval algebra is one of the most well-known calculi in qualitative temporal reasoning with numerous applications in artificial intelligence. Recently, there has been a surge of improvements in the fine-grained complexity of…