Separations between Oblivious and Adaptive Adversaries for Natural Dynamic Graph Problems
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2025
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| author | Bernstein, Aaron Bhattacharya, Sayan Fischer, Nick Kiss, Peter Saranurak, Thatchaphol |
| author_facet | Bernstein, Aaron Bhattacharya, Sayan Fischer, Nick Kiss, Peter Saranurak, Thatchaphol |
| contents | We establish the first update-time separation between dynamic algorithms against oblivious adversaries and those against adaptive adversaries in natural dynamic graph problems, based on popular fine-grained complexity hypotheses. Specifically, under the combinatorial BMM hypothesis, we show that every combinatorial algorithm against an adaptive adversary for the incremental maximal independent set problem requires $n^{1-o(1)}$ amortized update time. Furthermore, assuming either the 3SUM or APSP hypotheses, every algorithm for the decremental maximal clique problem needs $Δ/n^{o(1)}$ amortized update time when the initial maximum degree is $Δ\le \sqrt{n}$. These lower bounds are matched by existing algorithms against adaptive adversaries. In contrast, both problems admit algorithms against oblivious adversaries that achieve $\operatorname{polylog}(n)$ amortized update time [Behnezhad, Derakhshan, Hajiaghayi, Stein, Sudan; FOCS '19] [Chechik, Zhang; FOCS '19]. Therefore, our separations are exponential. Previously known separations for dynamic algorithms were either engineered for contrived problems and relied on strong cryptographic assumptions [Beimel, Kaplan, Mansour, Nissim, Saranurak, Stemmer; STOC '22], or worked for problems whose inputs are not explicitly given but are accessed through oracle calls [Bateni, Esfandiari, Fichtenberger, Henzinger, Jayaram, Mirrokni, Wiese; SODA '23].
As a byproduct, we also provide a separation between incremental and decremental algorithms for the triangle detection problem: we show a decremental algorithm with $\tilde{O}(n^ω)$ total update time, while every incremental algorithm requires $n^{3-o(1)}$ total update time, assuming the OMv hypothesis. To our knowledge this is the first separation of this kind. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20341 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Separations between Oblivious and Adaptive Adversaries for Natural Dynamic Graph Problems Bernstein, Aaron Bhattacharya, Sayan Fischer, Nick Kiss, Peter Saranurak, Thatchaphol Data Structures and Algorithms We establish the first update-time separation between dynamic algorithms against oblivious adversaries and those against adaptive adversaries in natural dynamic graph problems, based on popular fine-grained complexity hypotheses. Specifically, under the combinatorial BMM hypothesis, we show that every combinatorial algorithm against an adaptive adversary for the incremental maximal independent set problem requires $n^{1-o(1)}$ amortized update time. Furthermore, assuming either the 3SUM or APSP hypotheses, every algorithm for the decremental maximal clique problem needs $Δ/n^{o(1)}$ amortized update time when the initial maximum degree is $Δ\le \sqrt{n}$. These lower bounds are matched by existing algorithms against adaptive adversaries. In contrast, both problems admit algorithms against oblivious adversaries that achieve $\operatorname{polylog}(n)$ amortized update time [Behnezhad, Derakhshan, Hajiaghayi, Stein, Sudan; FOCS '19] [Chechik, Zhang; FOCS '19]. Therefore, our separations are exponential. Previously known separations for dynamic algorithms were either engineered for contrived problems and relied on strong cryptographic assumptions [Beimel, Kaplan, Mansour, Nissim, Saranurak, Stemmer; STOC '22], or worked for problems whose inputs are not explicitly given but are accessed through oracle calls [Bateni, Esfandiari, Fichtenberger, Henzinger, Jayaram, Mirrokni, Wiese; SODA '23]. As a byproduct, we also provide a separation between incremental and decremental algorithms for the triangle detection problem: we show a decremental algorithm with $\tilde{O}(n^ω)$ total update time, while every incremental algorithm requires $n^{3-o(1)}$ total update time, assuming the OMv hypothesis. To our knowledge this is the first separation of this kind. |
| title | Separations between Oblivious and Adaptive Adversaries for Natural Dynamic Graph Problems |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2510.20341 |