The Online House Numbering Problem: Min-Max Online List Labeling

We introduce and study the online house numbering problem, where houses are added arbitrarily along a road and must be assigned labels to maintain their ordering along the road. The online house numbering problem is related to classic online list labeling problems, except that the optimization goal here is to minimize the maximum number of times that any house is relabeled. We provide several algorithms that achieve interesting tradeoffs between upper bounds on the number of maximum relabels per element and the number of bits used by labels

Nonlocal mechanism for cluster synchronization in neural circuits

The interplay between the topology of cortical circuits and synchronized activity modes in distinct cortical areas is a key enigma in neuroscience. We present a new nonlocal mechanism governing the periodic activity mode: the greatest common divisor (GCD) of network loops. For a stimulus to one node, the network splits into GCD-clusters in which cluster neurons are in zero-lag synchronization. For complex external stimuli, the number of clusters can be any common divisor. The synchronized mode and the transients to synchronization pinpoint the type of external stimuli. The findings, supported by an information mixing argument and simulations of Hodgkin Huxley population dynamic networks with unidirectional connectivity and synaptic noise, call for reexamining sources of correlated activity in cortex and shorter information processing time scales.Comment: 8 pges, 6 figure

Property matching and weighted matching

AbstractIn many pattern matching applications the text has some properties attached to its various parts. Pattern Matching with Properties (Property Matching, for short), involves a string matching between the pattern and the text, and the requirement that the text part satisfies some property. Some immediate examples come from molecular biology where it has long been a practice to consider special areas in the genome by their structures.It is straightforward to do sequential matching in a text with properties. However, indexing in a text with properties becomes difficult if we desire the time to be output dependent. We present an algorithm for indexing a text with properties in O(nlog|Σ|+nloglogn) time for preprocessing and O(|P|log|Σ|+toccπ) per query, where n is the length of the text, P is the sought pattern, Σ is the alphabet, and toccπ is the number of occurrences of the pattern that satisfy some property π.As a practical use of Property Matching we show how to solve Weighted Matching problems using techniques from Property Matching. Weighted sequences have recently been introduced as a tool to handle a set of sequences that are not identical but have many local similarities. The weighted sequence is a “statistical image” of this set, where we are given the probability of every symbol’s occurrence at every text location. Weighted matching problems are pattern matching problems where the given text is weighted.We present a reduction from Weighted Matching to Property Matching that allows off-the-shelf solutions to numerous weighted matching problems including indexing, swapped matching, parameterized matching, approximate matching, and many more. Assuming that one seeks the occurrence of pattern P with probability ϵ in weighted text T of length n, we reduce the problem to a property matching problem of pattern P in text T′ of length O(n(1ϵ)2log1ϵ)