Related papers: A Static Optimality Transformation with Applicatio…
In this work, we define the problem of finding an optimal query plan as finding spanning trees with low costs. This approach empowers the utilization of a series of spanning tree algorithms, thereby enabling systematic exploration of the…
Optimal motion planning involves obstacles avoidance where path planning is the key to success in optimal motion planning. Due to the computational demands, most of the path planning algorithms can not be employed for real-time based…
Self-adjusting data structures are a classic approach to adapting the complexity of operations to the data access distribution. While several self-adjusting variants are known for both binary search trees and B-Trees, existing constructions…
We present a method to find globally optimal topology and trajectory jointly for planar linkages. Planar linkage structures can generate complex end-effector trajectories using only a single rotational actuator, which is very useful in…
The paper deals with optimality issues in connection with updating beliefs in networks. We address two processes: triangulation and construction of junction trees. In the first part, we give a simple algorithm for constructing an optimal…
Answering complex logical queries on incomplete knowledge graphs is a challenging task, and has been widely studied. Embedding-based methods require training on complex queries, and cannot generalize well to out-of-distribution query…
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…
In this paper, we consider several efficient data structures for the problem of sampling from a dynamically changing discrete probability distribution, where some prior information is known on the distribution of the rates, in particular…
Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which…
One popular technique to solve temporal planning problems consists in decoupling the causal decisions, demanding them to heuristic search, from temporal decisions, demanding them to a simple temporal network (STN) solver. In this…
This report investigates three fundamental search algorithms: Linear Search, Binary Search, and Two Pointer Search. Linear Search checks each element sequentially, Binary Search divides the search space in half, and Two Pointer Search uses…
We describe an algorithm that takes as input n points in the plane and a parameter {\epsilon}, and produces as output an embedded planar graph having the given points as a subset of its vertices in which the graph distances are a (1 +…
A central challenge in scaling up explicit state-space search for large tasks is compactly representing the set of generated states. Tree databases, a data structure from model checking, require constant space per generated state in the…
Path planning is an important component in any highly automated vehicle system. In this report, the general problem of path planning is considered first in partially known static environments where only static obstacles are present but the…
The connection of edges in a graph generates a structure that is independent of a coordinate system. This visual metaphor allows creating a more flexible representation of data than a two-dimensional scatterplot. In this work, we present…
Optimal transport is a fundamental topic that has attracted a great amount of attention from the optimization community in the past decades. In this paper, we consider an interesting discrete dynamic optimal transport problem: can we…
Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…
Answering connectivity queries is fundamental to fully dynamic graphs where edges and vertices are inserted and deleted frequently. Existing work proposes data structures and algorithms with worst-case guarantees. We propose a new data…
We consider preprocessing a set $S$ of $n$ points in convex position in the plane into a data structure supporting queries of the following form: given a point $q$ and a directed line $\ell$ in the plane, report the point of $S$ that is…
Spatial data is ubiquitous. Massive amounts of data are generated every day from a plethora of sources such as billions of GPS-enabled devices (e.g., cell phones, cars, and sensors), consumer-based applications (e.g., Uber and Strava), and…