10675163
Maximal and Minimal Vertex-Critical Graphs of Diameter Two
A graph is vertex-critical if deleting any vertex increases its diameter. We construct, for each??5 except?=6, a vertex-critical graph of diameter two on?vertices with at least 12?2?2?3/2+c1?edges, wherec1is some constant. We show that such a graph contains at most 12?2?(2/2)?3/2+c2?edges, wherec2is some constant. We also construct, for each??5 except?=6, a vertex-critical graph of diameter two on?vertices with at most 12 (5??12) edges. We show that such a graph must contain at least 12 (5??29) edges.
4333882
Linear-Time Representation Algorithms for Proper Circular-Arc Graphs and Proper Interval Graphs
Our main result is a linear-time (that is, time $O(m+n)$) algorithm to recognize and represent proper circular-arc graphs. The best previous algorithm, due to A. Tucker, has time complexity $O(n^2)$. We take advantage of the fact that (among connected graphs) proper circular-arc graphs are precisely the graphs orientable as local tournaments, and we use a new characterization of local tournaments. The algorithm depends on repeated representation of portions of the input graph as proper interval graphs. Thus we also find it useful to give a new linear-time algorithm to represent proper interval graphs. This latter algorithm also depends on an orientation characterization of proper interval graphs. It is conceptually simple and does not use complex data structures. As a byproduct of the correctness proof of the algorithm, we also obtain a new proof of a characterization of proper interval graphs by forbidden subgraphs.
31025959
A Note on Spanning Local Tournaments in Locally Semicomplete Digraphs
We prove a result which implies that every k-connected locally semicomplete digraph which is not a semicomplete digraph must contain a k-connected spanning local tournament. This improves an earlier result of Guo and partially answers a question of Jackson and Thomassen.
10979198
Weakly Hamiltonian-connected ordinary multipartite tournaments
Abstract We characterize weakly Hamiltonian-connected ordinary multipartite tournaments. Our result generalizes such a characterization for tournaments by Thomassen and implies a polynomial algorithm to decide the existence of a Hamiltonian path connecting two given vertices in an ordinary multipartite tournament and finds one, if it exists.
4789976
In-Tournament Digraphs
Abstract In this paper we introduce a generalization of digraphs that are locally tournaments (and hence of tournaments). This is the class of in-tournament digraphs-the set of predecessors of every vertex induces a tournament. We show that many properties of local tournament digraphs can be extended even to in-tournament digraphs. For instance, any strongly connected in-tournament digraph has a directed hamiltonian cycle. We prove that the underlying graph of any in-tournament digraph is l-homotopic. We investigate the problem of which graphs are orientable as in-tournament digraphs and prove that any graph representable as an intersection subgraph of a unicyclic graph can be so oriented. It is shown that there is a polynomial algorithm for recognizing those graphs that can be oriented as in-tournament digraphs.
4803217
Pushing the cycles out of multipartite tournaments
Abstract Let D be a digraph and X ⊆ V ( D ). By pushing X we mean reversing each arc of D with exactly one end in X. Klostermeyer proved that it is NP-complete to decide if a given digraph can be made acyclic using the push operation. Here we characterize, in terms of forbidden subdigraphs, the multipartite tournaments which can be made acyclic (resp. ordinary, unidirectional) using the push operation. This implies that the problem of deciding if a given multipartite tournament can be made acyclic (resp. ordinary, unidirectional) using the push operation and, if so, finding a suitable subset of vertices to push, is solvable in polynomial time.
16721854
Learning from labeled and unlabeled data on a directed graph
We propose a general framework for learning from labeled and unlabeled data on a directed graph in which the structure of the graph including the directionality of the edges is considered. The time complexity of the algorithm derived from this framework is nearly linear due to recently developed numerical techniques. In the absence of labeled instances, this framework can be utilized as a spectral clustering method for directed graphs, which generalizes the spectral clustering approach for undirected graphs. We have applied our framework to real-world web classification problems and obtained encouraging results.
392551
Finding Target Language Correspondence for Lexicalized EBMT System
This paper presents a three-phase approach to find the correspondence in Target Language (TL) sentence for a fragment of Source Language (SL) sentence in a lexicalized EBMT system. To be practical, it exploits surface information as much as possible instead of using parsers. Experiments show that, although not so perfect, it is very robust and effective. The three phases are: First, align the sentence pair at word level in order to provide anchors for phrase alignment. Second, based on the aligned anchors, find all the TL fragments which may possibly correspond to a SL fragment. And finally, using a score function, select the best TL fragment as the correspondence of a SL fragment.
7488499
Chinese-Korean Word Alignment Based on Linguistic Comparison
Word alignment problem between parallel corpora is based on the similar characteristics of two aligned words in two languages. We investigate linguistic-knowledge-based word similarity measures while other previous works heavily rely on statistical information, and their limits will be discussed. Linguistic knowledge is acquired from linguistic comparison of all layers between two languages, for Chinese and Korean in this paper.
6920930
Data Broadcast on a Multi-System Heterogeneous Overlayed Wireless Network
We propose in this paper a two-phase algorithm, named algorithm layered-cutting, to address the problem of broadcast program generation in a multisystem heterogeneous overlayed wireless network. The experimental results show that algorithm layered-cutting is able to efficiently generate broadcast programs of high quality for a multisystem heterogeneous overlayed wireless network
8925570
Auction-Based Spectrum Sharing
We study auction mechanisms for sharing spectrum among a group of users, subject to a constraint on the interference temperature at a measurement point. The users access the channel using spread spectrum signaling and so interfere with each other. Each user receives a utility that is a function of the received signal-to-interference plus noise ratio. We propose two auction mechanisms for allocating the received power. The first is an auction in which users are charged for received SINR, which, when combined with logarithmic utilities, leads to a weighted max-min fair SINR allocation. The second is an auction in which users are charged for power, which maximizes the total utility when the bandwidth is large enough and the receivers are co-located. Both auction mechanisms are shown to be socially optimal for a limiting “large system” with co-located receivers, where bandwidth, power and the number of users are increased in fixed proportion. We also formulate an iterative and distributed bid updating algorithm, and specify conditions under which this algorithm converges globally to the Nash equilibrium of the auction.