The Edge Group Coloring Problem with Applications to Multicast Switching

This paper introduces a natural generalization of the classical edge coloring problem in graphs that provides a useful abstraction for two well-known problems in multicast switching. We show that the problem is NP-hard and evaluate the performance of several approximation algorithms, both analytically and experimentally. We find that for random $\chi$-colorable graphs, the number of colors used by the best algorithms falls within a small constant factor of $\chi$, where the constant factor is mainly a function of the ratio of the number of outputs to inputs. When this ratio is less than 10, the best algorithms produces solutions that use fewer than $2\chi$ colors. In addition, one of the algorithms studied finds high quality approximate solutions for any graph with high probability, where the probability of a low quality solution is a function only of the random choices made by the algorithm

Faster Maximium Priority Matchings in Bipartite Graphs

A maximum priority matching is a matching in an undirected graph that maximizes a priority score defined with respect to given vertex priorities. An earlier paper showed how to find maximum priority matchings in unweighted graphs. This paper describes an algorithm for bipartite graphs that is faster when the number of distinct priority classes is limited. For graphs with $k$ distinct priority classes it runs in $O(kmn^{1/2})$ time, where $n$ is the number of vertices in the graph and $m$ is the number of edges

Grafalgo - A Library of Graph Algorithms and Supporting Data Structures (revised)

This report provides an (updated) overview of {\sl Grafalgo}, an open-source library of graph algorithms and the data structures used to implement them. The programs in this library were originally written to support a graduate class in advanced data structures and algorithms at Washington University. Because the code's primary purpose was pedagogical, it was written to be as straightforward as possible, while still being highly efficient. Grafalgo is implemented in C++ and incorporates some features of C++11. The library is available on an open-source basis and may be downloaded from https://code.google.com/p/grafalgo/. Source code documentation is at www.arl.wustl.edu/\textasciitilde jst/doc/grafalgo. While not designed as production code, the library is suitable for use in larger systems, so long as its limitations are understood. The readability of the code also makes it relatively straightforward to extend it for other purposes

The Bounded Edge Coloring Problem and Offline Crossbar Scheduling

This paper introduces a variant of the classical edge coloring problem in graphs that can be applied to an offline scheduling problem for crossbar switches. We show that the problem is NP-complete, develop three lower bounds bounds on the optimal solution value and evaluate the performance of several approximation algorithms, both analytically and experimentally. We show how to approximate an optimal solution with a worst-case performance ratio of $3/2$ and our experimental results demonstrate that the best algorithms produce results that very closely track a lower bound

Search for ttˉt\bar{t} resonances in semileptonic final states in pp collisions at s\sqrt{s} = 8 TeV

A search for the production of new heavy resonances produced in proton-proton collisions at the CMS Experiment that decay into top quark pairs is presented. Data was recorded at a center of mass energy of 8 TeV and corresponds to an integrated luminosity of 19.6 fb$^{-1}$. Results are presented as a combination of two dedicated searches, the first optimized for kinematic threshold production of top quark pairs and the second optimized for a highly boosted regime. No excess is observed above the expected yield from SM processes. In the absence of any excess we set the following limits at 95% CL on the production of non-SM particles. Top color Z' bosons with relative widths of 1.2% and 10% are excluded for masses below 2.10 TeV and 2.68 TeV. Upper limits of 1.94 pb and 0.029 pb are set on the production cross section times branching fraction for narrow resonances with masses of 0.5 TeV and 2 TeV. Likewise, limits of 1.71 pb and 0.045 pb are set for wide resonances with masses of 0.5 TeV and 2 TeV. In addition, Kaluza-Klein excitations of a gluon with masses below 2.54 TeV in the Randall-Sundrum model are excluded and an upper limit of 0.101 pb is set for a resonance mass of 2 TeV.Comment: Presentation at the DPF 2013 Meeting of the American Physical Society Division of Particles and Fields, Santa Cruz, California, August 13-17, 201

Issues In Distributed Control For Atm Networks

Asynchronous Transfer Mode (ATM) network technology is expected to become a central part of the emerging global information infrastructure. ATM networks introduce a number of features that distinguish them from earlier technologies and introduce new issues in network control. This paper offers a framework for precisely defining and analyzing alternative approaches to the distributed control of ATM networks and explores some of the key design issues through a series of examples. It is hoped that it will provide a useful foundation for researchers in networking and distributed computing interested in exploring these issues further and developing more complete solutions. 0 This work was supported by the ARPA Computing Systems Technology Office, Ascom Timeplex, Bay Networks, Bell Northern Research, NEC, NTT, Southwestern Bell and Tektronix. ISSUES IN DISTRIBUTED CONTROL FOR ATM NETWORKS Jonathan S. Turner Washington University, St. Louis [email protected] 1. Introduction Asynchronous T..

Maximum Priority Matchings

Let G=(V,E) be an undirected graph with n vertices and m edges, in which each vertex u is assigned an integer priority in [1,n], with 1 being the ``highest\u27\u27 priority. Let M be a matching of G. We define the priority score of M to be an n-ary integer in which the i-th most-significant digit is the number of vertices with priority i that are incident to an edge in M. We describe a variation of the augmenting path method (Edmonds\u27 algorithm) that finds a matching with maximum priority score in O(mn) time

Grafalgo - A Library of Graph Algorithms and Supporting Data Structures

This report provides an overview of Grafalgo, an open-source library of graph algorithms and the data structures used to implement them. The programs in this library were originally written to support a graduate class in advanced data structures and algorithms at Washington University. Because the code\u27s primary purpose was pedagogical, it was written to be as straightforward as possible, while still being highly efficient. Grafalgo is implemented in C++ and incorporates some features of C++11. The library is available on an open-source basis and may be downloaded from https://code.google.com/p/grafalgo/. Source code documentation is at www.arl.wustl.edu/~jst/doc/grafalgo. While not designed as production code, the library is suitable for use in larger systems, so long as its limitations are understood. The readability of the code also makes it relatively straightforward to extend it for other purposes