Deciding the On-line Chromatic Number of a Graph with Pre-Coloring is PSPACE-Complete

The problem of determining if the on-line chromatic number of a graph is less than or equal to k, given a pre-coloring, is shown to be PSPACE-complete

Advice Complexity of the Online Induced Subgraph Problem

Several well-studied graph problems aim to select a largest (or smallest) induced subgraph with a given property of the input graph. Examples include maximum independent set, maximum planar graph, maximum clique, minimum feedback vertex set, and many others. In online versions of these problems, the vertices of the graph are presented in an adversarial order, and with each vertex, the online algorithm must irreversibly decide whether to include it into the constructed subgraph, based only on the subgraph induced by the vertices presented so far. We study the properties that are common to all these problems by investigating a generalized problem: for an arbitrary but fixed hereditary property pi, find some maximal induced subgraph having pi. We investigate this problem from the point of view of advice complexity, i.e., we ask how some additional information about the yet unrevealed parts of the input can influence the solution quality. We evaluate the information in a quantitative way by considering the best possible advice of given size that describes the unknown input. Using a result from Boyar et al. [STACS 2015, LIPIcs 30], we give a tight trade-off relationship stating that, for inputs of length n, roughly n/c bits of advice are both needed and sufficient to obtain a solution with competitive ratio c, regardless of the choice of pi, for any c (possibly a function of n). This complements the results from Bartal et al. [SIAM Journal on Computing 36(2), 2006] stating that, without any advice, even a randomized algorithm cannot achieve a competitive ratio better than Omega(n^{1-log_{4}3-o(1)}). Surprisingly, for a given cohereditary property pi and the objective to find a minimum subgraph having pi, the advice complexity varies significantly with the choice of pi. We also consider a preemptive online model, inspired by some applications mainly in networking and scheduling, where the decision of the algorithm is not completely irreversible. In particular, the algorithm may discard some vertices previously assigned to the constructed set, but discarded vertices cannot be reinserted into the set. We show that, for the maximum induced subgraph problem, preemption does not significantly help by giving a lower bound of Omega(n/(c^2log c)) on the bits of advice that are needed to obtain competitive ratio c, where c is any increasing function bounded from above by sqrt(n/log n). We also give a linear lower bound for c close to 1

Advice Complexity of the Online Induced Subgraph Problem

Several well-studied graph problems aim to select a largest (or smallest) induced subgraph with a given property of the input graph. Examples of such problems include maximum independent set, maximum planar graph, and many others. We consider these problems, where the vertices are presented online. With each vertex, the online algorithm must decide whether to include it into the constructed subgraph, based only on the subgraph induced by the vertices presented so far. We study the properties that are common to all these problems by investigating the generalized problem: for a hereditary property \pty, find some maximal induced subgraph having \pty. We study this problem from the point of view of advice complexity. Using a result from Boyar et al. [STACS 2015], we give a tight trade-off relationship stating that for inputs of length n roughly n/c bits of advice are both needed and sufficient to obtain a solution with competitive ratio c, regardless of the choice of \pty, for any c (possibly a function of n). Surprisingly, a similar result cannot be obtained for the symmetric problem: for a given cohereditary property \pty, find a minimum subgraph having \pty. We show that the advice complexity of this problem varies significantly with the choice of \pty. We also consider preemptive online model, where the decision of the algorithm is not completely irreversible. In particular, the algorithm may discard some vertices previously assigned to the constructed set, but discarded vertices cannot be reinserted into the set again. We show that, for the maximum induced subgraph problem, preemption cannot help much, giving a lower bound of $\Omega(n/(c^2\log c))$ bits of advice needed to obtain competitive ratio $c$, where $c$ is any increasing function bounded by \sqrt{n/log n}. We also give a linear lower bound for c close to 1

The Advice Complexity of a Class of Hard Online Problems

The advice complexity of an online problem is a measure of how much knowledge of the future an online algorithm needs in order to achieve a certain competitive ratio. Using advice complexity, we define the first online complexity class, AOC. The class includes independent set, vertex cover, dominating set, and several others as complete problems. AOC-complete problems are hard, since a single wrong answer by the online algorithm can have devastating consequences. For each of these problems, we show that $\log\left(1+(c-1)^{c-1}/c^{c}\right)n=\Theta (n/c)$ bits of advice are necessary and sufficient (up to an additive term of $O(\log n)$) to achieve a competitive ratio of $c$. The results are obtained by introducing a new string guessing problem related to those of Emek et al. (TCS 2011) and B\"ockenhauer et al. (TCS 2014). It turns out that this gives a powerful but easy-to-use method for providing both upper and lower bounds on the advice complexity of an entire class of online problems, the AOC-complete problems. Previous results of Halld\'orsson et al. (TCS 2002) on online independent set, in a related model, imply that the advice complexity of the problem is $\Theta (n/c)$. Our results improve on this by providing an exact formula for the higher-order term. For online disjoint path allocation, B\"ockenhauer et al. (ISAAC 2009) gave a lower bound of $\Omega (n/c)$ and an upper bound of $O((n\log c)/c)$ on the advice complexity. We improve on the upper bound by a factor of $\log c$. For the remaining problems, no bounds on their advice complexity were previously known.Comment: Full paper to appear in Theory of Computing Systems. A preliminary version appeared in STACS 201

Large-Scale Analysis of B-Cell Epitopes on Influenza Virus Hemagglutinin – Implications for Cross-Reactivity of Neutralizing Antibodies

Influenza viruses continue to cause substantial morbidity and mortality worldwide. Fast gene mutation on surface proteins of influenza virus result in increasing resistance to current vaccines and available antiviral drugs. Broadly neutralizing antibodies (bnAbs) represent targets for prophylactic and therapeutic treatments of influenza. We performed a systematic bioinformatics study of cross-reactivity of neutralizing antibodies (nAbs) against influenza virus surface glycoprotein hemagglutinin (HA). This study utilized the available crystal structures of HA complexed with the antibodies for the analysis of tens of thousands of HA sequences. The detailed description of B-cell epitopes, measurement of epitope area similarity among different strains, and estimation of antibody neutralizing coverage provide insights into cross-reactivity status of existing nAbs against influenza virus. We have developed a method to assess the likely cross-reactivity potential of bnAbs for influenza strains, either newly emerged or existing. Our method catalogs influenza strains by a new concept named discontinuous peptide, and then provide assessment of cross-reactivity. Potentially cross-reactive strains are those that share 100% identity with experimentally verified neutralized strains. By cataloging influenza strains and their B-cell epitopes for known bnAbs, our method provides guidance for selection of representative strains for further experimental design. The knowledge of sequences, their B-cell epitopes, and differences between historical influenza strains, we enhance our preparedness and the ability to respond to the emerging pandemic threats

BlockLogo: Visualization of peptide and sequence motif conservation

BlockLogo is a web-server application for the visualization of protein and nucleotide fragments, continuous protein sequence motifs, and discontinuous sequence motifs using calculation of block entropy from multiple sequence alignments. The user input consists of a multiple sequence alignment, selection of motif positions, type of sequence, and output format definition. The output has BlockLogo along with the sequence logo, and a table of motif frequencies. We deployed BlockLogo as an online application and have demonstrated its utility through examples that show visualization of T-cell epitopes and B-cell epitopes (both continuous and discontinuous). Our additional example shows a visualization and analysis of structural motifs that determine the specificity of peptide binding to HLA-DR molecules. The BlockLogo server also employs selected experimentally validated prediction algorithms to enable on-the-fly prediction of MHC binding affinity to 15 common HLA class I and class II alleles as well as visual analysis of discontinuous epitopes from multiple sequence alignments. It enables the visualization and analysis of structural and functional motifs that are usually described as regular expressions. It provides a compact view of discontinuous motifs composed of distant positions within biological sequences. BlockLogo is available at: http://research4.dfci.harvard.edu/cvc/blocklogo/ and http://met-hilab.bu.edu/blocklogo/

FluKB: A Knowledge-Based System for Influenza Vaccine Target Discovery and Analysis of the Immunological Properties of Influenza Viruses

FluKB is a knowledge-based system focusing on data and analytical tools for influenza vaccine discovery. The main goal of FluKB is to provide access to curated influenza sequence and epitope data and enhance the analysis of influenza sequence diversity and the analysis of targets of immune responses. FluKB consists of more than 400,000 influenza protein sequences, known epitope data (357 verified T-cell epitopes, 685 HLA binders, and 16 naturally processed MHC ligands), and a collection of 28 influenza antibodies and their structurally defined B-cell epitopes. FluKB was built using a modular framework allowing the implementation of analytical workflows and includes standard search tools, such as keyword search and sequence similarity queries, as well as advanced tools for the analysis of sequence variability. The advanced analytical tools for vaccine discovery include visual mapping of T-and B-cell vaccine targets and assessment of neutralizing antibody coverage. FluKB supports the discovery of vaccine targets and the analysis of viral diversity and its implications for vaccine discovery as well as potential T-cell breadth and antibody cross neutralization involving multiple strains. FluKB is representation of a new generation of databases that integrates data, analytical tools, and analytical workflows that enable comprehensive analysis and automatic generation of analysis reports

State of the art : children’s cognition and nonverbal communication

FluKB is a knowledge-based system focusing on data and analytical tools for influenza vaccine discovery. The main goal of FluKB is to provide access to curated influenza sequence and epitope data and enhance the analysis of influenza sequence diversity and the analysis of targets of immune responses. FluKB consists of more than 400,000 influenza protein sequences, known epitope data (357 verified T-cell epitopes, 685 HLA binders, and 16 naturally processed MHC ligands), and a collection of 28 influenza antibodies and their structurally defined B-cell epitopes. FluKB was built using a modular framework allowing the implementation of analytical workflows and includes standard search tools, such as keyword search and sequence similarity queries, as well as advanced tools for the analysis of sequence variability. The advanced analytical tools for vaccine discovery include visual mapping of T- and B-cell vaccine targets and assessment of neutralizing antibody coverage. FluKB supports the discovery of vaccine targets and the analysis of viral diversity and its implications for vaccine discovery as well as potential T-cell breadth and antibody cross neutralization involving multiple strains. FluKB is representation of a new generation of databases that integrates data, analytical tools, and analytical workflows that enable comprehensive analysis and automatic generation of analysis reports