32727998
Equitable Coloring of Trees
Abstract A graph is equitably k -colorable if its vertices can be partitioned into k independent sets of as near equal sizes as possible. Regarding a non-null tree T as a bipartite graph T ( X , Y ), we show that T is equitably k -colorable if and only if (i) k ≥ 2 when | | X | − | Y | | ≤ 1; (ii) k ≥ max{3, ⌈(| T | + 1)/(α( T − N [ v ]) + 2)⌉} when | | X | − | Y | | > 1. In case (ii), v is an arbitrary vertex of maximum degree in T and the number α( T − N [ v ]) denotes the independence number of the subgraph of T obtained by deleting v and all its adjacent vertices.
16166391
Linear k-arboricities on trees
Abstract For a fixed positive integer k, the linear k-arboricity lak(G) of a graph G is the minimum number l such that the edge set E(G) can be partitioned into l disjoint sets and that each induces a subgraph whose components are paths of lengths at most k. This paper studies linear k-arboricity from an algorithmic point of view. In particular, we present a linear-time algorithm to determine whether a tree T has lak(T)⩽m.
16547141
Edge domination in complete partite graphs
Abstract An edge dominating set in a graph G is a set of edges D such that every edge not in D is adjacent to an edge of D . An edge domatic partition of a graph G =( V , E ) is a collection of pairwise-disjoint edge dominating sets of G whose union is E . The maximum size of an edge domatic partition of G is called the edge domatic number . In this paper, we study the edge domatic number of the complete partite graphs and give the answers for balanced complete partite graphs and complete split graphs .
14354011
A study of the total chromatic number of equibipartite graphs
Abstract The total chromatic number χ t ( G ) of a graph G is the least number of colors needed to color the vertices and edges of G so that no adjacent vertices or edges receive the same color, no incident edges receive the same color as either of the vertices it is incident with. In this paper, we obtain some results of the total chromatic number of the equibipartite graphs of order 2 n with maximum degree n − 1. As a part of our results, we disprove the biconformability conjecture.
42366271
A Note on the m-Bounded Chromatic Number of a Tree
Abstract The m-bounded chromatic number of a graph G is the smallest number of colors required for a proper coloring of G in which each color is used at most m times. We will establish an exact formula for the m -bounded chromatic number of a tree.
12831347
Equitable Coloring and the Maximum Degree
Abstract Let Δ(G) denote the maximum degree of a graph G . The equitable Δ-coloring conjecture asserts that a connected graph G is equitably Δ( G )-colorable if it is different from K m , C 2 m + 1 and K 2 m + 1,2 m + 1 for all m ⩾ 1. This conjecture is established for graphs G satisfying Δ( G ) ⩾ | G |/2 or Δ( G ) ⩽ 3.
1980658
Geometric Sieving: Automated Distributed Optimization of 3D Motifs for Protein Function Prediction
Determining the function of all proteins is a recurring theme in modern biology and medicine, but the sheer number of proteins makes experimental approaches impractical. For this reason, current efforts have considered in silico function prediction in order to guide and accelerate the function determination process. One approach to predicting protein function is to search functionally uncharacterized protein structures (targets), for substructures with geometric and chemical similarity (matches), to known active sites (motifs). Finding a match can imply that the target has an active site similar to the motif, suggesting functional homology. 
 
An effective function predictor requires effective motifs – motifs whose geometric and chemical characteristics are detected by comparison algorithms within functionally homologous targets (sensitive motifs), which also are not detected within functionally unrelated targets (specific motifs). Designing effective motifs is a difficult open problem. Current approaches select and combine structural, physical, and evolutionary properties to design motifs that mirror functional characteristics of active sites. 
 
We present a new approach, Geometric Sieving (GS), which refines candidate motifs into optimized motifs with maximal geometric and chemical dissimilarity from all known protein structures. The paper discusses both the usefulness and the efficiency of GS. We show that candidate motifs from six well-studied proteins, including α-Chymotrypsin, Dihydrofolate Reductase, and Lysozyme, can be optimized with GS to motifs that are among the most sensitive and specific motifs possible for the candidate motifs. For the same proteins, we also report results that relate evolutionarily important motifs with motifs that exhibit maximal geometric and chemical dissimilarity from all known protein structures. Our current observations show that GS is a powerful tool that can complement existing work on motif design and protein function prediction.
15709443
Voice retrieval of Mandarin broadcast news speech
This paper presents an improved framework for voice retrieval of Mandarin broadcast news speech. First, several unsupervised and data-driven approaches for broadcast news transcription were proposed to improve the speech recognition accuracy and efficiency. Then, a multiscale indexing paradigm for broadcast news retrieval was exploited to alleviate the problems caused by the speech recognition errors and the flexible wording structure of the Chinese language. Finally, we used the PDA as the platform and broadcast radio programs collected in Taiwan as the document collection to establish a speech-based multimedia information retrieval prototype system. Very encouraging results were obtained.
4000197
Lot-sizing scheduling with batch setup times
This paper is concerned with scheduling independent jobs on m parallel machines in such a way that the makespan is minimized. Each job j is allowed to split arbitrarily into several parts, which can be individually processed on any machine at any time. However, a setup for uninterrupted sj time units is required before any split part of job j can be processed on any machine. The problem is strongly NP-hard if the number m of machines is variable and weakly NP-hard otherwise. We give a polynomial-time $$\frac{5}{3}$$-approximation algorithm for the former case and a fully polynomial-time approximation scheme for the latter.
607529
Toward a Query Language for Network Attack Data
The growing sophistication and diversity of malicious activity in the Internet presents a serious challenge for network security analysts. In this paper, we describe our efforts to develop a database and query language for network attack data from firewalls, intrusion detection systems and honeynets. Our first step toward this objective is to develop a prototype database and query interface to identify coordinated scanning activity in network attack data. We have created a set of aggregate views and templatized SQL queries that consider timing, persistence, targeted services, spatial dispersion and temporal dispersion, thereby enabling us to evaluate coordinated scanning along these dimensions. We demonstrate the utility of the interface by conducting a case study on a set of firewall and intrusion detection system logs from Dshield.org. We show that the interface is able to identify general characteristics of coordinated activity as well as instances of unusual activity that would otherwise be difficult to mine from the data. These results highlight the potential for developing a more generalized query language for a broad class of network intrusion data. The case study also exposes some of the challenges we face in extending our system to more generalized queries over potentially vast quantities of data.
13073706
Graph homotopy and Graham homotopy
Abstract Simple-homotopy for cell complexes is a special type of topological homotopy constructed by elementary collapses and elementary expansions. In this paper, we introduce graph homotopy for graphs and Graham homotopy for hypergraphs and study the relation between the two homotopies and the simple-homotopy for cell complexes. The graph homotopy is useful to describe topological properties of discretized geometric figures, while the Graham homotopy is essential to characterize acyclic hypergraphs and acyclic relational database schemes.