We initiate the study of graph sketching, i.e., algorithms that use a limited number of linear measurements of a graph to determine the properties of the graph. While a graph on n nodes is essentially O(n2)-dimensional, we show the existence of a distribution over random projections into d-dimensional "sketch" space (d « n2) such that several relevant properties of the original graph can be inf...

In a linear forest, each component is a path. The linear arboricity ~(G) of a graph G is defined in Harary [8] as the minimum number of linear forests whose union is G. This invariant first arose in a study [i0] of information retrieval in file systems. A quite similar covering invariant which is well known to the linear arboricity is the arboricity of a graph, which is defined as the minimum n...

Given a mental picture Ĝ = (V, Ê) of some unknown graph G = (V,E), how can we verify that our mental image is correct, when the unknown graph is only accessible by querying pairs of vertices and getting their shortest path distance in G? For graphs of bounded degree, we give an algorithm that uses a number of queries that is at most O(log n) times the minimum number achievable. For graphs that ...

A sequence of graphs Gn is iteratively constructible if it can be built from an initial labeled graph by means of a repeated fixed succession of elementary operations involving addition of vertices and edges, deletion of edges, and relabelings. Let Gn be a iteratively constructible sequence of graphs. In a recent paper, [27], M. Noy and A. Ribò have proven linear recurrences with polynomial coe...

Computer vision is a rich source of important yet intractable optimization problems. Over the past decade, researchers have shown that many such problems can be efficiently solved by graph cuts. Graph cut algorithms combine elegant theoretical properties with compelling experimental results. I will focus on the difficult but important challenge of solving rank-deficient linear inverse systems. ...

The determination of drug or hormone concentrations by radioimmunoassay involves interpolation of values for radioisotope counts within standard curves, a technique which requires some dexterity in curve drawing and which results in some inaccuracy in practice. A number of linear transformations (Ekins, 1974) and computer programs (Burger et al, 1972; Duddleson et al, 1972; Livesey, 1974) for s...

Graph-based Fisher Analysis (GbFA) is proposed recently for dimensionality reduction, which has the powerful discriminant ability. However, GbFA is based on the matrix-to-vector way, which not only costs much but also loses spatial relations of pixels in images. Therefore, Tensor Graph-based Linear Discriminant Analysis (TGbLDA) is proposed in the paper. TGbLDA regards samples as data in tensor...

The linear complexity of a matrix is a measure of the number of additions, subtractions, and scalar multiplications required to multiply that matrix and an arbitrary vector. In this paper, we define the linear complexity of a graph to be the linear complexity of any one of its associated adjacency matrices. We then compute or give upper bounds for the linear complexity of several classes of gra...

The objective often explored in Web-based route planners is to find an optimal route in a network for a given mode of transport. Usually this involves searching for the cheapest route corresponding to some cost function. For many types of trips, not all desired route properties can be satisfied in this way. Following is a proposed solution for planning hiking trips. The method can easily be tra...

Batagelj and Zaversnik proposed a linear algorithm for the wellknown k-core decomposition problem. However, when k-cores are desired for a given k, we find that a simple linear algorithm requiring no sorting works for mining k-cores. In addition, this algorithm can be extended to mine (k1, k2, . . . , kp)-cores from p-partite graphs in linear time, and this mining approach can be efficiently im...