Distance queries over dynamic interval graphs

Jingbang Chen, Meng He, J. Ian Munro, Richard Peng, Kaiyu Wu, Daniel J. Zhang

Abstract: Highlights•Fully dynamic proper interval graph with O(log⁡n)<math><mi is="true">O</mi><mo stretchy="false" is="true">(</mo><mi mathvariant="normal" is="true">log</mi><mo is="true">⁡</mo><mi is="true">n</mi><mo stretchy="false" is="true">)</mo></math> time operations.•Incremental and decremental interval graph with O(log⁡n)<math><mi is="true">O</mi><mo stretchy="false" is="true">(</mo><mi mathvariant="normal" is="true">log</mi><mo is="true">⁡</mo><mi is="true">n</mi><mo stretchy="false" is="true">)</mo></math> amortized time operations.•Fully dynamic interval graph with O(nlog⁡n)<math><mi is="true">O</mi><mo stretchy="false" is="true">(</mo><msqrt is="true"><mrow is="true"><mi is="true">n</mi><mi mathvariant="normal" is="true">log</mi><mo is="true">⁡</mo><mi is="true">n</mi></mrow></msqrt><mo stretchy="false" is="true">)</mo></math> time operations.