41044254
On the dependence polynomial of a graph
The dependence polynomial PG = PG(z) of a graph G is defined by PG(z) := Σi=0n (-1)icizi where ci = ci(G) is the number of complete subgraphs of G of cardinality i. It is clear that the complete subgraphs of G form a poset relative to subset inclusion. Using Mobius inversion, this yields various identities involving dependence polynomials implying in particular that the dependence polynomial of the line graph L(G) of G is determined uniquely by the (multiset of) vertex degrees of G and the number of triangles in G. Furthermore, the dependence polynomial of the complement of the line graph of G is closely related to the matching polynomial of G, one of the most 'prominent' polynomials studied in graph theory.
207130271
Frobenius maps
A graph is called Frobenius if it is a connected orbital regular graph of a Frobenius group. A Frobenius map is a regular Cayley map whose underlying graph is Frobenius. In this paper, we show that almost all low-rank Frobenius graphs admit regular embeddings and enumerate non-isomorphic Frobenius maps for a given Frobenius graph. For some Frobenius groups, we classify all Frobenius maps derived from these groups. As a result, we construct some Frobenius maps with trivial exponent groups as a partial answer of a question raised by Nedela and Skoviera (Exponents of orientable maps, Proc. London Math. Soc. 75(3) (1997) 1-31).
10079260
The sum number and integral sum number of complete bipartite graphs
Let N denote the set of positive integers. The sum graph G + (S) of a 1nite subset S of N is the graph (S; E) with vertex set S and edge set E such that for u; v ∈ S; uv ∈ E if and only if u + v ∈ S. A graph G is called a sum graph if it is isomorphic to the sum graph G + (S) of some 1nite subset S of N . The sum number � (G) of a graph G is de1ned as the smallest nonnegative integer m for which G ∪ mK1 is a sum graph. Let Z be the set of all integers. By extending the set N to Z in the above de1nitions of sum graphs and sum numbers, Harary [3] introduced the corresponding notions of integral sum graphs and integral sum number of a graph. In this paper, we evaluate the value of the sum number and integral sum number of the complete bipartite graph Kr; s. While the former one corrects the result given in [4], the latter settles completely a problem proposed in [3]. c � 2001 Elsevier Science B.V. All rights reserved.
122817250
Modeling complex motion by tracking and editing hidden Markov graphs
We propose a generative model for representing complex motion, such as wavy river, dancing fire and dangling cloth. Our generative method consists of four components: (1) A photometric model using primal sketch[8] which transfers an image into an attribute graph representation. Each vertex of the graph is a scaled and oriented image patch selected from a dictionary. The graph connects and aligns these patches. (2) A geometric model which characterizes the deformation of the attribute graph. (3) A dynamic model, which specifies the motion dynamics of these vertices (patches) and their interactions in the form of coupled Markov chains. (4) A topological model, which interprets the graph topological changes over time. We learn this generative model by a stochastic gradient algorithm implemented by Markov Chain Monte Carlo (MCMC) sampling. This method is shown to be effective in handling the topological changes of graphs. The correctness of the learned model is verified by the low-dimension reconstruction of the original image as well as by the realistic motion sequences it synthesized.
18269009
Maximum Flows and Critical Vertices in AND/OR Graphs
We will study this problem and present an algorithm for finding the minimum-time-cost solution graph in an AND/OR graph. We will also study the following problems which often appear in industry when using AND/OR graphs to model manufacturing processes or to model problem solving processes: finding maximum (additive and nonadditive) flows and critical vertices in an AND/OR graph. Though there are well known polynomial time algorithms for the corresponding problems in the traditional graph theory, we will show that generally it is NP-hard to find a non-additive maximum flow in an AND/OR graph, and it is both NP-hard and coNP-hard to find a set of critical vertices in an AND/OR graph. We will also present a polynomial time algorithm for finding a maximum additive flow in an AND/OR graph, and discuss the relative complexity of these problems.
2187866
Synchronous distance education: enhancing speaking skills via Internet-based real time technology
The paper reports on an investigation into one of the most urgent problems facing distance language education: the problem of lack of exposure to speaking practice in the target language. The Open Learning Chinese Program taught at Griffith University is used as a case study. Following a discussion on issues relating to distance education for languages such as the indispensability of technology to learning languages in a distance mode, and the importance of communicative competence, the paper moves on to an examination of the capabilities of Internet based real time technology. Two major indications can be generated from this research: real time technology can help solve the problem of insufficient exposure to speaking practice, and a historical convergence of distance and traditional campus based education toward a networked education can be expected.
2865514
MARio: mobility-adaptive routing using route lifetime abstractions in mobile ad hoc networks
Mobile Ad hoc NETworks (MANETs) often have fast-changing and unpredictable mobility. This is especially true for recently emerging mobile sensor networks [7] and delay tolerant networks [2], where extreme network conditions are prevalent. To better adjust to such network conditions, we propose to deconstruct the underlying node mobility into a set of abstractions that can be readily leveraged for driving dynamic routing decisions. In particular, we investigate the feasibility of using route lifetime to abstract mobility. Through extensive simulations on DSR, we demonstrate up to 31% improvement in packet delivery rate and 53% improvement in average end-to-end packet latency, using our proposed route prefetch and decay techniques that leverage knowledge of route lifetimes.
14856574
Error Resilient Video Coding Using Unequally Protected Key Pictures
This paper proposes the use of unequally protected key pictures to prevent temporal error propagation in error-prone video communications. The key picture may either be an intra-coded picture or a picture using a long-term motion compensation reference picture through reference picture selection. The inter-coded key picture uses previous key pictures as motion compensation reference. Key pictures are better protected than other pictures using forward error correction in either source or transport coding. Simulation results show significantly improved error resiliency performance of the proposed technique compared to conventional methods.