Related papers: Least Squares Ranking on Graphs
The minimum skew rank $mr^{-}(\mathbb{F},G)$ of a graph $G$ over a field $\mathbb{F}$ is the smallest possible rank among all skew symmetric matrices over $\mathbb{F}$, whose ($i$,$j$)-entry (for $i\neq j$) is nonzero whenever $ij$ is an…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
In this paper, we study the problem of finding the least square solutions of over-determined linear algebraic equations over networks in a distributed manner. Each node has access to one of the linear equations and holds a dynamic state. We…
We analyze the problem of packing squares in an online fashion: Given a semi-infinite strip of width 1 and an unknown sequence of squares of side length in [0,1] that arrive from above, one at a time. The objective is to pack these items as…
The minimum rank of a simple graph $G$ is defined to be the smallest possible rank over all symmetric real matrices whose $ij$th entry (for $i\neq j$) is nonzero whenever $\{i,j\}$ is an edge in $G$ and is zero otherwise. Minimum rank is a…
The minimum rank problem is to determine for a graph $G$ the smallest rank of a Hermitian (or real symmetric) matrix whose off-diagonal zero-nonzero pattern is that of the adjacency matrix of $G$. Here $G$ is taken to be a circulant graph,…
Resource allocation and scheduling are a common problem in various distributed systems. Although widely studied, the state-of-the-art solutions either do not scale or lack the expressive power to capture the most complex instances of the…
In this paper, we study Ranking, a well-known randomized greedy matching algorithm, for general graphs. The algorithm was originally introduced by Karp, Vazirani, and Vazirani [STOC 1990] for the online bipartite matching problem with…
In this work we present the notion of greyscale of a graph as a colouring of its vertices that uses colours from the real interval [0,1]. Any greyscale induces another colouring by assigning to each edge the non-negative difference between…
A $k$-ranking of a graph $G$ is a labeling of its vertices from $\{1,\ldots,k\}$ such that any nontrivial path whose endpoints have the same label contains a larger label. The least $k$ for which $G$ has a $k$-ranking is the ranking number…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
We study theoretical and computational aspects of the least squares fit (LSF) of circles and circular arcs. First we discuss the existence and uniqueness of LSF and various parametrization schemes. Then we evaluate several popular circle…
Many important values for cooperative games are known to arise from least square optimization problems. The present investigation develops an optimization framework to explain and clarify this phenomenon in a general setting. The main…
Multicriteria Decision Making problems are important both for individuals and groups. Pairwise comparisons have become popular in the theory and practice of preference modelling and quantification. We focus on decision problems where the…
The adjacency matrix is the most fundamental and intuitive object in graph analysis that is useful not only mathematically but also for visualizing the structures of graphs. Because the appearance of an adjacency matrix is critically…
The bottom-left algorithm is a simple heuristic for the Strip Packing Problem. It places the rectangles in the given order at the lowest free position in the strip, using the left most position in case of ties. Despite its simplicity, the…
Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…
The paper suggests a family of paired comparison-based scoring procedures for ranking the participants of a Swiss system chess team tournament. We present the challenges of ranking in Swiss system, the features of individual and team…
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…