| Autor: |
Christiansen, Aleksander B. G., Rotenberg, Eva, Steiner, Teresa Anna, Vlieghe, Juliette |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
Differential privacy is the gold standard in the problem of privacy preserving data analysis, which is crucial in a wide range of disciplines. Vertex colouring is one of the most fundamental questions about a graph. In this paper, we study the vertex colouring problem in the differentially private setting. To be edge-differentially private, a colouring algorithm needs to be defective: a colouring is d-defective if a vertex can share a colour with at most d of its neighbours. Without defectiveness, the only differentially private colouring algorithm needs to assign n different colours to the n different vertices. We show the following lower bound for the defectiveness: a differentially private c-edge colouring algorithm of a graph of maximum degree {\Delta} > 0 has defectiveness at least d = {\Omega} (log n / (log c+log {\Delta})). We also present an {\epsilon}-differentially private algorithm to {\Theta} ( {\Delta} / log n + 1 / {\epsilon})-colour a graph with defectiveness at most {\Theta}(log n). |
| Databáze: |
arXiv |
| Externí odkaz: |
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