Related papers: Computing Maximal Chains

We prove a number of results related to the computational complexity of recognizing well-covered graphs. Let $k$ and $s$ be positive integers and let $G$ be a graph. Then $G$ is said - $\mathbf{W_k}$ if for any $k$ pairwise disjoint…

Well-structured systems, aka WSTSs, are computational models where the set of possible configurations is equipped with a well-quasi-ordering which is compatible with the transition relation between configurations. This structure supports…

In the paper we present results to develop an irreducible theory of complex systems in terms of self-organization processes of prime integer relations. Based on the integers and controlled by arithmetic only the self-organization processes…

In multivariate or spatial extremes, inference for max-stable processes observed at a large collection of locations is among the most challenging problems in computational statistics, and current approaches typically rely on less expensive…

The problem of determining whether a probabilistic program terminates almost surely (i.e.~with probability one) is undecidable, and actually $\Pi^0_2$-complete. For this reason, a growing literature has explored classes of programs for…

This paper considers large families of Markov chains (MCs) that are defined over a set of parameters with finite discrete domains. Such families occur in software product lines, planning under partial observability, and sketching of…

In 1952, Littlewood stated a conjecture about the average growth of spherical derivatives of polynomials, and showed that it would imply that for entire function of finite order, "most" preimages of almost all points are concentrated in a…

Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations.…

When you first heard people speak of Piles of PCs, the first thing that came to mind may have been a cluttered computer room with processors, monitors, and snarls of cables all around. Collections of computers have undoubtedly become more…

Separating hash families are useful combinatorial structures which generalize several well-studied objects in cryptography and coding theory. Let $p_t(N, q)$ denote the maximum size of universe for a $t$-perfect hash family of length $N$…

We study the optimization version of constraint satisfaction problems (Max-CSPs) in the framework of parameterized complexity; the goal is to compute the maximum fraction of constraints that can be satisfied simultaneously. In standard…

Let $X$ be a finite set in a complex sphere of $d$ dimension. Let $D(X)$ be the set of usual inner products of two distinct vectors in $X$. A set $X$ is called a complex spherical $s$-code if the cardinality of $D(X)$ is $s$ and $D(X)$…

Many social networks and complex systems are found to be naturally divided into clusters of densely connected nodes, known as community structure (CS). Finding CS is one of fundamental yet challenging topics in network science. One of the…

We present an exposition of the *Chain Bounding Lemma*, which is a common generalization of both Zorn's Lemma and the Bourbaki-Witt fixed point theorem. The proofs of these results through the use of Chain Bounding are amongst the simplest…

Let $L$ be a set of $n$ lines in the plane, not necessarily in general position. We present an efficient algorithm for finding all the vertices of the arrangement $A(L)$ of maximum level, where the level of a vertex $v$ is the number of…

Let (W, S) be a Coxeter system. We investigate combinatorially certain partial orders, called extended Bruhat orders, on a (W x W)-set W(N,C), which depends on W, a subset N of S, and a component C of N. We determine the length of the…

We prove simple theorems concerning the maximal order of a large class of multiplicative functions. As an application, we determine the maximal orders of certain functions of the type $\sigma_A(n)= \sum_{d\in A(n)} d$, where A(n) is a…

One way of getting a better view of data is using frequent patterns. In this paper frequent patterns are subsets that occur a minimal number of times in a stream of itemsets. However, the discovery of frequent patterns in streams has always…

Motivated by the concept of well-covered graphs, we define a graph to be well-bicovered if every vertex-maximal bipartite subgraph has the same order (which we call the bipartite number). We first give examples of them, compare them with…

A matching $M$ of a graph $G$ is maximal if it is not a proper subset of any other matching in $G$. Maximal matchings are much less known and researched than their maximum and perfect counterparts. In particular, almost nothing is known…