The Power of Dynamic Distance Oracles: Efficient Dynamic Algorithms for the Steiner Tree

In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an $n$-vertex graph $G=(V,E,w)$ with positive real edge weights, and our goal is to maintain a tree which is a good approximation of the minimum Steiner tree spanning a terminal set $S \subseteq V$, which changes over time. The changes applied to the terminal set are either terminal additions (incremental scenario), terminal removals (decremental scenario), or both (fully dynamic scenario). Our task here is twofold. We want to support updates in sublinear $o(n)$ time, and keep the approximation factor of the algorithm as small as possible. We show that we can maintain a $(6+\varepsilon)$-approximate Steiner tree of a general graph in $\tilde{O}(\sqrt{n} \log D)$ time per terminal addition or removal. Here, $D$ denotes the stretch of the metric induced by $G$. For planar graphs we achieve the same running time and the approximation ratio of $(2+\varepsilon)$. Moreover, we show faster algorithms for incremental and decremental scenarios. Finally, we show that if we allow higher approximation ratio, even more efficient algorithms are possible. In particular we show a polylogarithmic time $(4+\varepsilon)$-approximate algorithm for planar graphs. One of the main building blocks of our algorithms are dynamic distance oracles for vertex-labeled graphs, which are of independent interest. We also improve and use the online algorithms for the Steiner tree problem.Comment: Full version of the paper accepted to STOC'1

Plasmonic hot spots reveal local conformational transitions induced by DNA double-strand breaks

DNA double-strand breaks (DSBs) are typical DNA lesions that can lead to cell death, translocations, and cancer-driving mutations. The repair process of DSBs is crucial to the maintenance of genomic integrity in all forms of life. However, the limitations of sensitivity and special resolution of analytical techniques make it difficult to investigate the local effects of chemotherapeutic drugs on DNA molecular structure. In this work, we exposed DNA to the anticancer antibiotic bleomycin (BLM), a damaging factor known to induce DSBs. We applied a multimodal approach combining (i) atomic force microscopy (AFM) for direct visualization of DSBs, (ii) surface-enhanced Raman spectroscopy (SERS) to monitor local conformational transitions induced by DSBs, and (iii) multivariate statistical analysis to correlate the AFM and SERS results. On the basis of SERS results, we identified that bands at 1050 cm−1 and 730 cm−1 associated with backbone and nucleobase vibrations shifted and changed their intensities, indicating conformational modifications and strand ruptures. Based on averaged SERS spectra, the PLS regressions for the number of DSBs caused by corresponding molar concentrations of bleomycin were calculated. The strong correlation (R2 = 0.92 for LV = 2) between the predicted and observed number of DSBs indicates, that the model can not only predict the number of DSBs from the spectra but also detect the spectroscopic markers of DNA damage and the associated conformational changes