Unit Interval Editing is Fixed-Parameter Tractable

Given a graph~$G$ and integers $k_1$, $k_2$, and~$k_3$, the unit interval editing problem asks whether $G$ can be transformed into a unit interval graph by at most $k_1$ vertex deletions, $k_2$ edge deletions, and $k_3$ edge additions. We give an algorithm solving this problem in time $2^{O(k\log k)}\cdot (n+m)$, where $k := k_1 + k_2 + k_3$, and $n, m$ denote respectively the numbers of vertices and edges of $G$. Therefore, it is fixed-parameter tractable parameterized by the total number of allowed operations. Our algorithm implies the fixed-parameter tractability of the unit interval edge deletion problem, for which we also present a more efficient algorithm running in time $O(4^k \cdot (n + m))$. Another result is an $O(6^k \cdot (n + m))$-time algorithm for the unit interval vertex deletion problem, significantly improving the algorithm of van 't Hof and Villanger, which runs in time $O(6^k \cdot n^6)$.Comment: An extended abstract of this paper has appeared in the proceedings of ICALP 2015. Update: The proof of Lemma 4.2 has been completely rewritten; an appendix is provided for a brief overview of related graph classe

A self-help intervention for reducing time to diagnosis in Indonesian women with breast cancer symptoms

Objective: We investigated the effectiveness of a self-help intervention named PERANTARA, which aims to improve adherence to diagnostic procedures among women with breast cancer (BC) symptoms to reduce the time to a definitive diagnosis. Methods: With a cluster randomized crossover design across four hospitals, PERANTARA and treatment as usual (TAU) or TAU only was provided at successive periods in a randomly determined order. The main outcome was the time between the first medical consultation and the definitive diagnosis. Secondary outcomes were BC knowledge, measured by the Breast Cancer Knowledge Test (BCKT); symptoms of anxiety and depression, measured by the Hospital Anxiety and Depression Scale (HADS); quality of life, measured by the World Health Organization Quality of Life-BREF (WHOQOL-BREF); and health status, measured by the EQ-5D-5L. A linear mixed model analysis was conducted to analyse the outcomes. Results: We recruited 132 women with BC symptoms from four hospitals; 67 participants were in the intervention group, and 65 participants were in the control group. PERANTARA reduced the time to definitive diagnosis by 13.3 days (M [SD]: 25.90 [23.20] in the intervention group vs 39.29 [35.10] in the control group