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Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…
Given an n-vertex graph G, a drawing of G in the plane is a mapping of its vertices into points of the plane, and its edges into continuous curves, connecting the images of their endpoints. A crossing in such a drawing is a point where two…
Motivated by hybrid graph representations, we introduce and study the following beyond-planarity problem, which we call $h$-Clique2Path Planarity: Given a graph $G$, whose vertices are partitioned into subsets of size at most $h$, each…
Conformant planning is the problem of finding a sequence of actions for achieving a goal in the presence of uncertainty in the initial state or action effects. The problem has been approached as a path-finding problem in belief space where…
Optimization over trained machine learning models has applications including: verification, minimizing neural acquisition functions, and integrating a trained surrogate into a larger decision-making problem. This paper formulates and solves…
A multiflow in a planar graph is uncrossed if its support paths do not cross. Recently such flows have played a role in approximation algorithms for maximum disjoint paths in "fully-planar" instances, where the combined supply-demand graph…
We define a special case of tree decompositions for planar graphs that respect a given embedding of the graph. We study the analogous width of the resulting decomposition we call the embedded-width of a plane graph. We show both upper…
Motivated by large-scale optimization problems arising in the context of machine learning, there have been several advances in the study of asynchronous parallel and distributed optimization methods during the past decade. Asynchronous…
Consider a graph drawn on a surface (for example, the plane minus a finite set of obstacle points), possibly with crossings. We provide an algorithm to decide whether such a drawing can be untangled, namely, if one can slide the vertices…
Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some period. Can we predict whether the system will eventually synchronize? Even with a known underlying graph…
The constrained synchronization problem (CSP) asks for a synchronizing word of a given input automaton contained in a regular set of constraints. It could be viewed as a special case of synchronization of a discrete event system under…
We give a combinatorial condition for the existence of efficient, LP-based FPT algorithms for a broad class of graph-theoretical optimisation problems. Our condition is based on the notion of biased graphs known from matroid theory.…
In this paper, we show that given a weighted, directed planar graph $G$, and any $\epsilon >0$, there exists a polynomial time and $O(n^{\frac{1}{2}+\epsilon})$ space algorithm that computes the shortest path between two fixed vertices in…
Graphs are widely used to model execution dependencies in applications. In particular, the NP-complete problem of partitioning a graph under constraints receives enormous attention by researchers because of its applicability in…
We provide theoretical foundations and computational tools for the systematic design of optimization-based control laws with constraints that have different priorities. By introducing the concept of prioritized intersections, we extend and…
The problem of synchronization over a group $\mathcal{G}$ aims to estimate a collection of group elements $G^*_1, \dots, G^*_n \in \mathcal{G}$ based on noisy observations of a subset of all pairwise ratios of the form $G^*_i {G^*_j}^{-1}$.…
This paper studies a class of multi-robot coordination problems where a team of robots aim to reach their goal regions with minimum time and avoid collisions with obstacles and other robots. A novel numerical algorithm is proposed to…
This paper first proposes an N-block PCPM algorithm to solve N-block convex optimization problems with both linear and nonlinear constraints, with global convergence established. A linear convergence rate under the strong second-order…
We study a well known noisy model of the graph isomorphism problem. In this model, the goal is to perfectly recover the vertex correspondence between two edge-correlated Erd\H{o}s-R\'{e}nyi random graphs, with an initial seed set of…
In this paper we study paramertized motion planning algorithms which provide universal and flexible solutions to diverse motion planning problems. Such algorithms are intended to function under a variety of external conditions which are…