Building on existing algorithms and results, we offer new insights and algorithms for various problems related to detecting maximal and maximum bicliques. Most of these results focus on graphs with small maximum degree, providing improved complexities when this parameter is constant; a common characteristic in real-world graphs.
Chondroitin sulfate (CS) is the most abundant and widely distributed glycosaminoglycan (GAG) in the human body. As a component of proteoglycans (PGs) it has numerous roles in matrix stabilization and cellular regulation. This chapter highlights the roles of CS and CS-PGs in the central and peripheral nervous systems (CNS/PNS). CS has specific cell regulatory roles that control tissue function and homeostasis. The CNS/PNS contains a diverse range of CS-PGs which direct the development of embryonic neural axonal networks, and the responses of neural cell populations in mature tissues to traumatic injury. Following brain trauma and spinal cord injury, a stabilizing CS-PG-rich scar tissue is laid down at the defect site to protect neural tissues, which are amongst the softest tissues of the human body. Unfortunately, the CS concentrated in gliotic scars also inhibits neural outgrowth and functional recovery. CS has well known inhibitory properties over neural behavior, and animal models of CNS/PNS injury have demonstrated that selective degradation of CS using chondroitinase improves neuronal functional recovery. CS-PGs are present diffusely in the CNS but also form denser regions of extracellular matrix termed perineuronal nets which surround neurons. Hyaluronan is immobilized in hyalectan CS-PG aggregates in these perineural structures, which provide neural protection, synapse, and neural plasticity, and have roles in memory and cognitive learning. Despite the generally inhibitory cues delivered by CS-A and CS-C, some CS-PGs containing highly charged CS disaccharides (CS-D, CS-E) or dermatan sulfate (DS) disaccharides that promote neural outgrowth and functional recovery. CS/DS thus has varied cell regulatory properties and structural ECM supportive roles in the CNS/PNS depending on the glycoform present and its location in tissue niches and specific cellular contexts. Studies on the fruit fly,Drosophila melanogasterand the nematodeCaenorhabditis eleganshave provided insightful information on neural interconnectivity and the role of the ECM and its PGs in neural development and in tissue morphogenesis in a whole organism environment.
We provide a deterministic CONGEST algorithm to constant factor approximate the minimum dominating set on graphs of bounded arboricity in $O(\log n)$ rounds. This improves over the well-known randomized algorithm of Lenzen and Wattenhofer[DISC2010] by making it a deterministic algorithm.
We give a local-to-global principle for relative entropy contraction in simplicial complexes. This is similar to the local-to-global principle for variances obtained by Alev and Lau (2020).
We show that the edit distance between two strings of length $n$ can be computed within a factor of $f(ε)$ in $n^{1+ε}$ time as long as the edit distance is at least $n^{1-δ}$ for some $δ(ε) > 0$.
For any finite group $G$, we give an arithmetic algorithm to compute generalized Discrete Fourier Transforms (DFTs) with respect to $G$, using $O(|G|^{ω/2 + ε})$ operations, for any $ε> 0$. Here, $ω$ is the exponent of matrix multiplication.
We propose an explanation of the structure of the best known sorting networks for 16 elements with respect to the complexity and to the depth due to Green and van Voorhis.
We pull together previously established graph-theoretical results to produce the algorithm in the paper's title. The glue are three easy elementary lemmas.
We define a new selection problem, \emph{Selecting with History}, which extends the secretary problem to a setting with historical information. We propose a strategy for this problem and calculate its success probability in the limit of a large sequence.
We give the first concise description of the fastest known suffix sorting algorithm in main memory, the DivSufSort by Yuta Mori. We then present an extension that also computes the LCP-array, which is competitive with the fastest known LCP-array construction algorithm.
In this paper, we give a simple characterization of a set of popular matchings defined by preference lists with ties. By employing our characterization, we propose a polynomial time algorithm for finding a minimum cost popular matching.
We show that schemes for sparsifying matrices based on iteratively resampling rows yield guarantees matching classic 'offline' sparsifiers (see e.g. Spielman and Srivastava [STOC 2008]). In particular, this gives a formal analysis of a scheme very similar to the one proposed by Kelner and Levin [TCS 2013].
A nCk sequence is a sequence of n-bit numbers with k bits set. Given such a sequence C, the difference sequence D of C is subject to certain regularities that make it possible to generate D in 2|C| time, and, hence, to generate C in 3|C| time.
We survey $k$-best enumeration problems and the algorithms for solving them, including in particular the problems of finding the $k$ shortest paths, $k$ smallest spanning trees, and $k$ best matchings in weighted graphs.
We present a polylogarithmic local computation matching algorithm which guarantees a $(1-\eps)$-approximation to the maximum matching in graphs of bounded degree.
We give a representation for labeled ordered trees that supports labeled queries such as finding the i-th ancestor of a node with a given label. Our representation is succinct, namely the redundancy is small-o of the optimal space for storing the tree. This improves the representation of He et al. which is succinct unless the entropy of the labels is small.
In the paper "How to select a looser'' Prodinger was analyzing an algorithm where $n$ participants are selecting a leader by flipping <underline>fair</underline> coins, where recursively, the 0-party (those who i.e. have tossed heads) continues until the leader is chosen. We give an answer to the question stated in the Prodinger's paper – what happens if not a 0-party is recursively looking for a leader but always a party with a smaller cardinality. We show the lower bound on the number of rounds of the greedy algorithm (for <underline>fair</underline> coin).
In the paper we discuss a technology based on Bernstein polynomials of asymptotic analysis of a class of binomial sums that arise in information theory. Our method gives a quick derivation of required sums and can be generalized to multinomial distributions. As an example we derive a formula for the entropy of multinomial distributions. Our method simplifies previous work of Jacquet, Szpankowski and Flajolet from 1999.