Roman Rabinovich

Roman Rabinovich, Ibrahim Jubran, Aaron Wetzler et al.

This paper presents a novel beacon light coding protocol, which enables fast and accurate identification of the beacons in an image. The protocol is provably robust to a predefined set of detection and decoding errors, and does not require any synchronization between the beacons themselves and the optical sensor. A detailed guide is then given for developing an optical tracking and localization system, which is based on the suggested protocol and readily available hardware. Such a system operates either as a standalone system for recovering the six degrees of freedom of fast moving objects, or integrated with existing SLAM pipelines providing them with error-free and easily identifiable landmarks. Based on this guide, we implemented a low-cost positional tracking system which can run in real-time on an IoT board. We evaluate our system's accuracy and compare it to other popular methods which utilize the same optical hardware, in experiments where the ground truth is known. A companion video containing multiple real-world experiments demonstrates the accuracy, speed, and applicability of the proposed system in a wide range of environments and real-world tasks. Open source code is provided to encourage further development of low-cost localization systems integrating the suggested technology at its navigation core.

Hanno von Bergen, Larissa Fastenau, Enna Gerhard et al.

We study solution discovery, where the goal is to obtain a feasible solution to a problem from an initial configuration by a bounded sequence of local moves. In many applications, however, the graph that defines which vertex sets are feasible is not the same as the graph that governs how tokens, agents, or resources may move. Existing models such as token sliding and token jumping typically do not distinguish the problem graph and the movement graph. Motivated by this mismatch, we introduce a directed weighted two-graph model that cleanly separates feasibility from movement. A problem graph specifies the desired combinatorial objects, while a movement graph specifies admissible relocations and their costs. This yields a flexible framework that captures asymmetry, heterogeneous movement constraints, and weighted transitions, while subsuming classical discovery models as special cases. We investigate this model through \textsc{Path Discovery} and \textsc{Shortest Path Discovery}, where the task is to realize a vertex set containing an $s$-$t$-path or a shortest $s$-$t$-path in the problem graph. These problems are particularly natural in applications, since directed and weighted shortest paths are among the most fundamental algorithmic primitives. At the same time, previous work has already shown that discovery can be computationally hard even when the underlying optimization problem is easy. Our results show that this phenomenon persists, and becomes especially rich, in the two-graph setting. We obtain a detailed complexity picture, identifying tractable cases as well as strong hardness results.