Boxicity of Leaf Powers

The boxicity of a graph G, denoted as boxi(G), is defined as the minimum integer t such that G is an intersection graph of axis-parallel t-dimensional boxes. A graph G is a k-leaf power if there exists a tree T such that the leaves of the tree correspond to the vertices of G and two vertices in G are adjacent if and only if their corresponding leaves in T are at a distance of at most k. Leaf powers are used in the construction of phylogenetic trees in evolutionary biology and have been studied in many recent papers. We show that for a k-leaf power G, boxi(G) a parts per thousand currency sign k-1. We also show the tightness of this bound by constructing a k-leaf power with boxicity equal to k-1. This result implies that there exist strongly chordal graphs with arbitrarily high boxicity which is somewhat counterintuitive.

Compression of Weighted Graphs

We propose to compress weighted graphs (networks), motivated by the observation that large networks of social, biological, or other relations can be complex to handle and visualize. In the process also known as graph simplication, nodes and (unweighted) edges are grouped to supernodes and superedges, respectively, to obtain a smaller graph. We propose models and algorithms for weighted graphs. The interpretation (i.e. decompression) of a compressed, weighted graph is that a pair of original nodes is connected by an edge if their supernodes are connected by one, and that the weight of an edge is approximated to be the weight of the superedge. The compression problem now consists of choosing supernodes, superedges, and superedge weights so that the approximation error is minimized while the amount of compression is maximized. In this paper, we formulate this task as the 'simple weighted graph compression problem'. We then propose a much wider class of tasks under the name of 'generalized weighted graph compression problem'. The generalized task extends the optimization to preserve longer-range connectivities between nodes, not just individual edge weights. We study the properties of these problems and propose a range of algorithms to solve them, with dierent balances between complexity and quality of the result. We evaluate the problems and algorithms experimentally on real networks. The results indicate that weighted graphs can be compressed efficiently with relatively little compression error.

Covalent attachment of two important dicopper(II) systems in a one-dimensional polymeric chain: An x-ray structure of [Cu2(en)2(OH)2·Cu2(O2CMe)4](PF6)2·0.5EtOH]α showing the shortest Cucdots, three dots, centeredCu Distance in the tetraacetato core

Reaction of Cu2(O2CMe)4(H2O)2 with 1,2-diaminoethane(en) in ethanol, followed by the addition of NH4PF6, led to the formation of a covalently linked 1D polymeric copper(II) title complex showing alternating [Cu2(en)2(OH)22+] and [Cu2(O2CMe)4] units in the chain and the shortest Cucdots, three dots, centeredCu separation of 2.558(2) Å in the tetraacetato core.

NUcache: A Multicore Cache Organization Based on Next-Use Distance

In this work, we propose a new organization for the last level shared cache of a rnulticore system. Our design is based on the observation that the Next-Use distance, measured in terms of intervening misses between the eviction of a line and its next use, for lines brought in by a given delinquent PC falls within a predictable range of values. We exploit this correlation to improve the performance of shared caches in multi-core architectures by proposing the NUcache organization.

New Approximation Algorithms for Minimum Cycle Bases of Graphs

We consider the problem of computing an approximate minimum cycle basis of an undirected non-negative edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space over F-2 generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of G. Cycle bases of low weight are useful in a number of contexts, e.g. the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. Although in most such applications any cycle basis can be used, a low weight cycle basis often translates to better performance and/or numerical stability. Despite the fact that the problem can be solved exactly in polynomial time, we design approximation algorithms since the performance of the exact algorithms may be too expensive for some practical applications. We present two new algorithms to compute an approximate minimum cycle basis. For any integer k >= 1, we give (2k - 1)-approximation algorithms with expected running time O(kmn(1+2/k) + mn((1+1/k)(omega-1))) and deterministic running time O(n(3+2/k) ), respectively. Here omega is the best exponent of matrix multiplication. It is presently known that omega < 2.376. Both algorithms are o(m(omega)) for dense graphs. This is the first time that any algorithm which computes sparse cycle bases with a guarantee drops below the Theta(m(omega) ) bound. We also present a 2-approximation algorithm with expected running time O(M-omega root n log n), a linear time 2-approximation algorithm for planar graphs and an O(n(3)) time 2.42-approximation algorithm for the complete Euclidean graph in the plane.

On Computation of Minimum Distance of Linear Block Codes Above 1/2 Rate Coding

The minimum distance of linear block codes is one of the important parameter that indicates the error performance of the code. When the code rate is less than 1/2, efficient algorithms are available for finding minimum distance using the concept of information sets. When the code rate is greater than 1/2, only one information set is available and efficiency suffers. In this paper, we investigate and propose a novel algorithm to find the minimum distance of linear block codes with the code rate greater than 1/2. We propose to reverse the roles of information set and parity set to get virtually another information set to improve the efficiency. This method is 67.7 times faster than the minimum distance algorithm implemented in MAGMA Computational Algebra System for a (80, 45) linear block code.

Distance measures on intersecting objects and their applications

Let A and B be two objects. We define measures to characterize the penetration of A and B when A boolean AND B not equal 0. We then present properties of the measures and efficient algorithms to compute them for planar and polyhedral objects. We explore applications of the measures and present some experimental results.

Potential-distance relationships of clay-water systems considering the Stern theory

This paper deals with the use of Stem theory as applied to a clay-water electrolyte system, which is more realistic to understand the force system at micro level man the Gouy-Chapman theory. The influence of the Stern layer on potential-distance relationship has been presented quantitatively for certain specified clay-water systems and the results are compared with the Gouy-Chapman model. A detailed parametric study concerning the number of adsorption spots on the clay platelet, the thickness of the Stern layer, specific adsorption potential and the value of dielectric constant of the pore fluid in the Stern layer, was carried out. This study investigates that the potential obtained at any distance using the Stern theory is higher than that obtained by the Gouy-Chapman theory. The hydrated size of the ion is found to have a significant influence on the potential-distance relationship for a given clay, pore fluid characteristics and valence of the exchangeable ion.

Chordal Bipartite Graphs with High Boxicity

The boxicity of a graph G is defined as the minimum integer k such that G is an intersection graph of axis-parallel k-dimensional boxes. Chordal bipartite graphs are bipartite graphs that do not contain an induced cycle of length greater than 4. It was conjectured by Otachi, Okamoto and Yamazaki that chordal bipartite graphs have boxicity at most 2. We disprove this conjecture by exhibiting an infinite family of chordal bipartite graphs that have unbounded boxicity.

Some results on the reconstruction problems. p-claw-free, chordal, and p4-reducible graphs

A claw is an induced subgraph isomorphic to K-1,K-3. The claw-point is the point of degree 3 in a claw. A graph is called p-claw-free when no p-cycle has a claw-point on it. It is proved that for p greater than or equal to 4, p-claw-free graphs containing at least one chordless p-cycle are edge reconstructible. It is also proved that chordal graphs are edge reconstructible. These two results together imply the edge reconstructibility of claw-free graphs. A simple proof of vertex reconstructibility of P-4-reducible graphs is also presented. (C) 1995 John Wiley and Sons, Inc.

The existence of homeomorphic subgraphs in chordal graphs

We establish conditions for the existence, in a chordal graph, of subgraphs homeomorphic to K-n (n greater than or equal to 3), K-m,K-n (m,n greater than or equal to 2), and wheels W-r (r greater than or equal to 3). Using these results, we develop a simple linear time algorithm for testing planarity of chordal graphs. We also show how these results lead to simple polynomial time algorithms for the Fixed Subgraph Homeomorphism problem on chordal graphs for some special classes of pattern graphs.

Photophysical and electrochemical redox properties of fixed distance porphyrin-quinone systems

A few fixed distance covalently linked porphyrin-quinone molecules have been synthesized in which a benzoquinone is directly attached to a meso/beta-pyrrole position of tri(phenyl/pentafluorophenyl)/tetraphenylporphyrins. The choice of fluoroarylporphyrins permit modulation of Delta G(ET) values for photoinduced electron-transfer reactions in these systems. All short distance porphyrin-quinone molecules showed efficient quenching of the porphyrin singlet excited state. The electrochemical redox data coupled with the steady-state and time-resolved singlet emission data are analysed to evaluate the dependence of Delta G(ET) values on the rate of electron transfer (k(ET)) in these systems. The meso-trifluoroarylporphyrin-quinones are found to be sensitive probes of the surrounding dielectric environment. Varying solvent polarity on the mechanism of fluorescence quenching and k(ET) values revealed that short donor-acceptor distance and the solvent dielectric relaxation properties play a dominant role. (C) 1999 Elsevier Science S.A. All rights reserved.

Performance issues of distance relays for shunt FACTS compensated transmission lines

In this paper, the performance of distance relays when applied to transmission system equipped with shunt FACTS device, Static Synchronous Compensator (STATCOM) is described. The aim of the proposed study is to evaluate the performance of distance relays when STATCOM is incorporated at the mid point of transmission lines for voltage control. A detailed model of STATCOM and its control strategy is presented. The presence of these devices significantly affects apparent impedance seen by the distance relays due to their rapid response to different power system configurations. The distance relay is evaluated for different loading conditions and for different fault locations. The faults are created during various pre-fault loading conditions. The studies are performed on 400KV and 132KV systems and the results are presented. Simulation studies are carried out using transient simulation software, PSCAD/EMTDC.

Acyclic Edge-Coloring of Planar Graphs

A proper edge-coloring with the property that every cycle contains edges of at least three distinct colors is called an acyclic edge-coloring. The acyclic chromatic index of a graph G, denoted. chi'(alpha)(G), is the minimum k such that G admits an acyclic edge-coloring with k colors. We conjecture that if G is planar and Delta(G) is large enough, then chi'(alpha) (G) = Delta (G). We settle this conjecture for planar graphs with girth at least 5. We also show that chi'(alpha) (G) <= Delta (G) + 12 for all planar G, which improves a previous result by Fiedorowicz, Haluszczak, and Narayan Inform. Process. Lett., 108 (2008), pp. 412-417].