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

An Efficient Implementation of Edmonds\u27 Algorithm for Maximum Matching on Graphs ; CU-CS-062-75

A matching on a graph is a set of edges, no two of which shared a vertex. A maximum matching contains the greatest number of edges possible. This paper presents an efficient implementation of Edmonds’ algorithm for finding a maximum matching. The computation time is proportional to V^3, where V is the number of vertices; previous implementation of Edmonds’ algorithm have computation time proportional to V^4. The implementation is based on a system of labels that encodes the structure of alternating paths

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(kmn1/2) time, where n is the number of vertices in the graph and m is the number of edges

Efficient Algorithms for Finding Maximal Matching in Graphs

This paper surveys the techniques used for designing the most efficient algorithms for finding a maximum cardinality or weighted matching in (general or bipartite) graphs. It also lists some open problems concerning possible improvements in existing algorithms and the existence of fast parallel algorithms for these problems

An efficient algorithmic approach for mass spectrometry-based disulfide connectivity determination using multi-ion analysis

<p>Abstract</p> <p>Background</p> <p>Determining the disulfide (S-S) bond pattern in a protein is often crucial for understanding its structure and function. In recent research, mass spectrometry (MS) based analysis has been applied to this problem following protein digestion under both partial reduction and non-reduction conditions. However, this paradigm still awaits solutions to certain algorithmic problems fundamental amongst which is the efficient matching of an exponentially growing set of putative S-S bonded structural alternatives to the large amounts of experimental spectrometric data. Current methods circumvent this challenge primarily through simplifications, such as by assuming only the occurrence of certain ion-types (<it>b</it>-ions and <it>y</it>-ions) that predominate in the more popular dissociation methods, such as collision-induced dissociation (<it>CID</it>). Unfortunately, this can adversely impact the quality of results.</p> <p>Method</p> <p>We present an algorithmic approach to this problem that can, with high computational efficiency, analyze multiple ions types (<it>a</it>, <it>b</it>, <it>b^o, b^*, c</it>, <it>x</it>, <it>y, y^o, y^*,</it> and <it>z</it>) and deal with complex bonding topologies, such as inter/intra bonding involving more than two peptides. The proposed approach combines an approximation algorithm-based search formulation with data driven parameter estimation. This formulation considers only those regions of the search space where the correct solution resides with a high likelihood. Putative disulfide bonds thus obtained are finally combined in a globally consistent pattern to yield the overall disulfide bonding topology of the molecule. Additionally, each bond is associated with a confidence score, which aids in interpretation and assimilation of the results.</p> <p>Results</p> <p>The method was tested on nine different eukaryotic Glycosyltransferases possessing disulfide bonding topologies of varying complexity. Its performance was found to be characterized by high efficiency (in terms of time and the fraction of search space considered), sensitivity, specificity, and accuracy. The method was also compared with other techniques at the state-of-the-art. It was found to perform as well or better than the competing techniques. An implementation is available at: <url>http://tintin.sfsu.edu/~whemurad/disulfidebond</url>.</p> <p>Conclusions</p> <p>This research addresses some of the significant challenges in MS-based disulfide bond determination. To the best of our knowledge, this is the first algorithmic work that can consider multiple ion types in this problem setting while simultaneously ensuring polynomial time complexity and high accuracy of results.</p