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Specifically, when the active set is sampled according to a\n                    <jats:italic>pairwise-independent<\/jats:italic>\n                    (PI) distribution, we show a\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$(1-o_k(1))$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mo>(<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>-<\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>o<\/mml:mi>\n                              <mml:mi>k<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mrow>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:mn>1<\/mml:mn>\n                              <mml:mo>)<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mo>)<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -selectable OCRS for uniform matroids of rank\n                    <jats:italic>k<\/jats:italic>\n                    , and\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\Omega (1)$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>\u03a9<\/mml:mi>\n                            <mml:mo>(<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>)<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -selectable OCRSes for laminar, graphic, cographic, transversal, and regular matroids. These imply prophet inequalities with the same ratios when the set of values is drawn according to a PI distribution. Our results complement recent work of Dughmi et al. [2] showing that no\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\omega (1\/k)$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>\u03c9<\/mml:mi>\n                            <mml:mo>(<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>\/<\/mml:mo>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo>)<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -selectable OCRS exists in the PI setting for general matroids of rank\n                    <jats:italic>k<\/jats:italic>\n                    .\n                  <\/jats:p>","DOI":"10.1007\/s10107-025-02253-w","type":"journal-article","created":{"date-parts":[[2025,7,10]],"date-time":"2025-07-10T10:05:44Z","timestamp":1752141944000},"page":"295-338","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Pairwise-independent contention resolution"],"prefix":"10.1007","volume":"216","author":[{"given":"Anupam","family":"Gupta","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinqiao","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gregory","family":"Kehne","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2907-7186","authenticated-orcid":false,"given":"Roie","family":"Levin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,7,10]]},"reference":[{"key":"2253_CR1","doi-asserted-by":"crossref","unstructured":"Gupta, A., Hu, J., Kehne, G., Levin, R.: Pairwise-independent contention resolution. 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