Related papers: ZDD-Based Algorithmic Framework for Solving Shorte…
Given a graph and two vertex sets satisfying a certain feasibility condition, a reconfiguration problem asks whether we can reach one vertex set from the other by repeating prescribed modification steps while maintaining feasibility. In…
Decision diagrams for classification have some notable advantages over decision trees, as their internal connections can be determined at training time and their width is not bound to grow exponentially with their depth. Accordingly,…
Optimization decomposition methods are a fundamental tool to develop distributed solution algorithms for large scale optimization problems arising in fields such as machine learning and optimal control. In this paper, we present an…
Networks are designed with functionality, security, performance, and cost in mind. Tools exist to check or optimize individual properties of a network. These properties may conflict, so it is not always possible to run these tools in series…
In this note, we consider the problem of finding a step-by-step transformation between two longest increasing subsequences in a sequence, namely Longest Increasing Subsequence Reconfiguration. We give a polynomial-time algorithm for…
Given a graph, the minimum dominating set (MinDS) problem is to identify a smallest set $D$ of vertices such that every vertex not in $D$ is adjacent to at least one vertex in $D$. The MinDS problem is a classic $\mathcal{NP}$-hard problem…
An ordered binary decision diagram (OBDD) is a directed acyclic graph that represents a Boolean function. OBDDs are also known as special cases of oblivious read-once branching programs in the field of complexity theory. Since OBDDs have…
We present the first results on the parameterized complexity of reconfiguration problems, where a reconfiguration version of an optimization problem $Q$ takes as input two feasible solutions $S$ and $T$ and determines if there is a sequence…
Supercomputers are equipped with an increasingly large number of cores to use computational power as a way of solving problems that are otherwise intractable. Unfortunately, getting serial algorithms to run in parallel to take advantage of…
Zero-suppressed binary decision diagrams (ZDDs) are a data structure representing Boolean functions, and one of the most successful variants of binary decision diagrams (BDDs). On the other hand, BDDs are also called branching programs in…
Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…
We develop an approach called bounded combinatorial reconfiguration for solving combinatorial reconfiguration problems based on Answer Set Programming (ASP). The general task is to study the solution spaces of source combinatorial problems…
We consider the computational complexity of reconfiguration problems, in which one is given two combinatorial configurations satisfying some constraints, and is asked to transform one into the other using elementary transformations, while…
Semidefinite programs (SDPs) -- some of the most useful and versatile optimization problems of the last few decades -- are often pathological: the optimal values of the primal and dual problems may differ and may not be attained. Such SDPs…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
We propose a general framework for end-to-end learning of data structures. Our framework adapts to the underlying data distribution and provides fine-grained control over query and space complexity. Crucially, the data structure is learned…
Given a static vertex-selection problem (e.g. independent set, dominating set) on a graph, we can define a corresponding temporally satisfying reconfiguration problem on a temporal graph which asks for a sequence of solutions to the…
In the first paper (part I) of this series of two, we introduce four novel definitions of the ODT problems: three for size-constrained trees and one for depth-constrained trees. These definitions are stated unambiguously through executable…
Reconfiguration schedules, i.e., sequences that gradually transform one solution of a problem to another while always maintaining feasibility, have been extensively studied. Most research has dealt with the decision problem of whether a…
This work considers a Motion Planning Problem with Dynamic Obstacles (MPDO) in 2D that requires finding a minimum-arrival-time collision-free trajectory for a point robot between its start and goal locations amid dynamic obstacles moving…