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Felix Bock

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math.CO Computer Vision physics.comp-ph quant-ph

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preprint2026arXiv

Quantum-Inspired Robust and Scalable SAR Object Classification

SAR image classification naturally has to deal with huge noise and a high dynamic range particularly requiring robust classification models. Additionally, the deployment of these models on edge devices, such as drones and military aircraft, requires a careful balance between model size and classification accuracy. This study explores the potential of tensor networks to meet these robustness requirements, specifically evaluating their resilience to data poisoning. Unlike previous works that concentrated on conventional neural networks for SAR object detection, this research focuses on the robustness and model reduction capabilities of tensor networks in object classification. Our findings indicate that tensor networks are adept at addressing both the challenges of robustness and the need for model efficiency, thereby contributing valuable insights to the ongoing discourse in radar applications and deep learning methodologies in general.

preprint2022arXiv

A bound on the dissociation number

The dissociation number ${\rm diss}(G)$ of a graph $G$ is the maximum order of a set of vertices of $G$ inducing a subgraph that is of maximum degree at most $1$ . Computing the dissociation number of a given graph is algorithmically hard even when restricted to subcubic bipartite graphs. For a graph $G$ with $n$ vertices, $m$ edges, $k$ components, and $c_1$ induced cycles of length $1$ modulo $3$ , we show ${\rm diss}(G)\geq n-\frac{1}{3}\Big(m+k+c_1\Big)$ . Furthermore, we characterize the extremal graphs in which every two cycles are vertex-disjoint.

preprint2022arXiv

Majority Edge-Colorings of Graphs

We propose the notion of a majority $k$ -edge-coloring of a graph $G$ , which is an edge-coloring of $G$ with $k$ colors such that, for every vertex $u$ of $G$ , at most half the edges of $G$ incident with $u$ have the same color. We show the best possible results that every graph of minimum degree at least $2$ has a majority $4$ -edge-coloring, and that every graph of minimum degree at least $4$ has a majority $3$ -edge-coloring. Furthermore, we discuss a natural variation of majority edge-colorings and some related open problems.

preprint2022arXiv

Relating dissociation, independence, and matchings

A dissociation set in a graph is a set of vertices inducing a subgraph of maximum degree at most $1$ . Computing the dissociation number ${\rm diss}(G)$ of a given graph $G$ , defined as the order of a maximum dissociation set in $G$ , is algorithmically hard even when $G$ is restricted to be bipartite. Recently, Hosseinian and Butenko proposed a simple $\frac{4}{3}$ -approximation algorithm for the dissociation number problem in bipartite graphs. Their result relies on the inequality ${\rm diss}(G)\leq\frac{4}{3}α(G-M)$ implicit in their work, where $G$ is a bipartite graph, $M$ is a maximum matching in $G$ , and $α(G-M)$ denotes the independence number of $G-M$ . We show that the pairs $(G,M)$ for which this inequality holds with equality can be recognized efficiently, and that a maximum dissociation set can be determined for them efficiently. The dissociation number of a graph $G$ satisfies $\max\{ α(G),2ν_s(G)\} \leq {\rm diss}(G)\leq α(G)+ν_s(G)\leq 2α(G)$ , where $ν_s(G)$ denotes the induced matching number of $G$ . We show that deciding whether ${\rm diss}(G)$ equals any of the four terms lower and upper bounding ${\rm diss}(G)$ is NP-hard.

preprint2022arXiv

Relating the independence number and the dissociation number

The independence number $α(G)$ and the dissociation number ${\rm diss}(G)$ of a graph $G$ are the largest orders of induced subgraphs of $G$ of maximum degree at most $0$ and at most $1$ , respectively. We consider possible improvements of the obvious inequality $2α(G)\geq {\rm diss}(G)$ . For connected cubic graphs $G$ distinct from $K_4$ , we show $5α(G)\geq 3{\rm diss}(G)$ , and describe the rich and interesting structure of the extremal graphs in detail. For bipartite graphs, and, more generally, triangle-free graphs, we also obtain improvements. For subcubic graphs though, the inequality cannot be improved in general, and we characterize all extremal subcubic graphs.

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Felix Bock

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5 publications

Quantum-Inspired Robust and Scalable SAR Object Classification

A bound on the dissociation number

Majority Edge-Colorings of Graphs

Relating dissociation, independence, and matchings

Relating the independence number and the dissociation number

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