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We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…
Despite significant progress in the theory and practice of program analysis, analysing properties of heap data has not reached the same level of maturity as the analysis of static and stack data. The spatial and temporal structure of stack…
Current approaches to scheduling workloads on heterogeneous systems with specialized accelerators often rely on manual partitioning, offloading tasks with specific compute patterns to accelerators. This method requires extensive…
Neural networks are increasingly used in robotics as policies, state transition models, state estimation models, or all of the above. With these components being learned from data, it is important to be able to analyze what behaviors were…
In a recent work, Esmer et al. describe a simple method - Approximate Monotone Local Search - to obtain exponential approximation algorithms from existing parameterized exact algorithms, polynomial-time approximation algorithms and, more…
We consider the problem of computing a Steiner tree of minimum cost under a hop constraint which requires the depth of the tree to be at most $k$. Our main result is an exact algorithm for metrics induced by graphs with bounded treewidth…
Distributed systems that manage and process graph-structured data internally solve a graph partitioning problem to minimize their communication overhead and query run-time. Besides computational complexity -- optimal graph partitioning is…
The Restricted Shortest Path (RSP) problem, also known as the Delay-Constrained Least-Cost (DCLC) problem, is an NP-hard bicriteria optimization problem on graphs with $n$ vertices and $m$ edges. In a graph where each edge is assigned a…
In the decremental single-source shortest paths (SSSP) problem, the input is an undirected graph $G=(V,E)$ with $n$ vertices and $m$ edges undergoing edge deletions, together with a fixed source vertex $s\in V$. The goal is to maintain a…
We provide a control-theoretic perspective on optimal tensor algorithms for minimizing a convex function in a finite-dimensional Euclidean space. Given a function $\Phi: \mathbb{R}^d \rightarrow \mathbb{R}$ that is convex and twice…
With the growing sizes of data structures allocated in heap, understanding the actual use of heap memory is critically important for minimizing cache misses and reclaiming unused memory. A static analysis aimed at this is difficult because…
A locally-optimal structure is a combinatorial structure such as a maximal independent set that cannot be improved by certain (greedy) local moves, even though it may not be globally optimal. It is trivial to construct an independent set in…
Genome assembly is a fundamental problem in Bioinformatics, where for a given set of overlapping substrings of a genome, the aim is to reconstruct the source genome. The classical approaches to solving this problem use assembly graphs, such…
Modern programming environments provide extensive support for inspecting, analyzing, and testing programs based on the algorithmic structure of a program. Unfortunately, support for inspecting and understanding runtime data structures…
We revisit the Stochastic Knapsack problem, where a policy-maker chooses an execution order for jobs with fixed values and stochastic running-times, aiming to maximize the value completed by a deadline. Dean et al. (FOCS'04) show that…
In many machine learning applications, it is necessary to meaningfully aggregate, through alignment, different but related datasets. Optimal transport (OT)-based approaches pose alignment as a divergence minimization problem: the aim is to…
Many discrete minimization problems, including various versions of the shortest path problem, can be efficiently solved by dynamic programming (DP) algorithms that are "pure" in that they only perform basic operations, as min, max, +, but…
We propose a novel notion of pointer race for concurrent programs manipulating a shared heap. A pointer race is an access to a memory address which was freed, and it is out of the accessor's control whether or not the cell has been…
Shortest path search is a core operation in graph-based applications, yet existing methods face important limitations. Classical algorithms such as Dijkstra's and A* become inefficient as graphs grow more complex, while index-based…
In optimization or machine learning problems we are given a set of items, usually points in some metric space, and the goal is to minimize or maximize an objective function over some space of candidate solutions. For example, in clustering…