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The All-Pairs Shortest Paths (APSP) problem is one of the fundamental problems in theoretical computer science. It asks to compute the distance matrix of a given $n$-vertex graph. We revisit the classical problem of maintaining the distance…
An algorithm on weighted graphs is called universally optimal if it is optimal for every input graph, in the worst case taken over all weight assignments. Informally, this means the algorithm is competitive even with algorithms that are…
Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical…
We study the selection problem, namely that of computing the $i$th order statistic of $n$ given elements. Here we offer a data structure called \emph{selectable sloppy heap} handling a dynamic version in which upon request: (i)~a new…
In this paper, how to efficiently find the optimal path in complex warehouse layout and make real-time decision is a key problem. This paper proposes a new method of Proximal Policy Optimization (PPO) and Dijkstra's algorithm, Proximal…
Fast training of large machine learning models requires distributed training on AI clusters consisting of thousands of GPUs. The efficiency of distributed training crucially depends on the efficiency of the network interconnecting GPUs in…
We consider the problem of scheduling $n$ jobs on $m$ uniform machines while minimizing the makespan ($Q||C_{\max}$) and maximizing the minimum completion time ($Q||C_{\min}$) in an online setting with migration of jobs. In this online…
We study optimal Multi-robot Path Planning (MPP) on graphs, in order to improve the efficiency of multi-robot system (MRS) in the warehouse-like environment. We propose a novel algorithm, OMRPP (One-way Multi-robot Path Planning) based on…
Downsampling and path planning are essential in robotics and autonomous systems, as they enhance computational efficiency and enable effective navigation in complex environments. However, current downsampling methods often fail to preserve…
Fixtures for constraining the movement of parts have been extensively investigated in robotics, since they are essential for using robots in automated manufacturing. This paper deals with the design and optimized synthesis of a special type…
Contraction Hierarchies is a successful speedup-technique to Dijkstra's seminal shortest path algorithm that has a convenient trade-off between preprocessing and query times. We investigate a shared-memory parallel implementation that uses…
A single-commodity congestion approximator for a graph is a compact data structure that approximately predicts the edge congestion required to route any set of single-commodity flow demands in a network. A hierarchical congestion…
This paper introduces the batch-parallel Compressed Packed Memory Array (CPMA), a compressed, dynamic, ordered set data structure based on the Packed Memory Array (PMA). Traditionally, batch-parallel sets are built on pointer-based data…
Perfect hash functions can potentially be used to compress data in connection with a variety of data management tasks. Though there has been considerable work on how to construct good perfect hash functions, there is a gap between theory…
A modified version of the Dijkstra algorithm using an inventive contraction hierarchy is proposed. The algorithm considers a directed acyclic graph with a conical or semi-circular structure for which a pair of edges is chosen iteratively…
All traditional methods of computing shortest paths depend upon edge-relaxation where the cost of reaching a vertex from a source vertex is possibly decreased if that edge is used. We introduce a method which maintains lower bounds as well…
In this paper, we show new data structures maintaining approximate shortest paths in sparse directed graphs with polynomially bounded non-negative edge weights under edge insertions. We give more efficient incremental…
We present a new heuristic point-to-point routing algorithm based on contraction hierarchies (CH). Given an epsilon >= 0, we can prove that the length of the path computed by our algorithm is at most (1+epsilon) times the length of the…
Priority queue, often implemented as a heap, is an abstract data type that has been used in many well-known applications like Dijkstra's shortest path algorithm, Prim's minimum spanning tree, Huffman encoding, and the branch-and-bound…
Explorable heap selection is the problem of selecting the $n$th smallest value in a binary heap. The key values can only be accessed by traversing through the underlying infinite binary tree, and the complexity of the algorithm is measured…