5906681
Circumferences of 2-Connected Claw-Free Graphs
30829488
Vertex pancyclism in claw-free graphs
Abstract In this paper, we show four sufficient conditions for vertex pancyclicity in claw-free graphs. These results improve, respectively, results of Broersma and Veldman, Gould and Jacobson, and Ryjacek. In particular, we prove that if G is a 3-connected claw-free graph such that the vertices of degree 1 of every induced bull have a common neighbor in G then every vertex of G is contained in a cycle of all possible lengths except for four and five. We conjecture that almost all pancyclic claw-free graphs with minimum degree at least three are vertex pancyclic.
29060290
Hamiltonian Cycles in N2-Locally Connected Claw-Free Graphs
41518374
Longest cycles in regular 2-connected claw-free graphs
In this paper, we show that every 2-connected, k-regular claw-free graph on n vertices contains a cycle of length at least min 4k?2, n (k?8), and this result is best possible.
9337355
Weather forecasting: predicting performance for streaming video over wireless LANs
The growth of wireless LANs has brought the expectation for high-bitrate streaming video to wireless PCs. However, it remains unclear how wireless channel characteristics impact the quality of streaming video sent over wireless LANs. This paper presents results from experiments that stream commercial video over a wireless campus network. By analyzing the streaming video quality and capturing wireless LAN characteristics across network and wireless link layers, "weather forecasts" are created such that selected wireless LAN performance indicators might be used to predict the streaming video quality. Furthermore, a quantified measurement of accuracy is presented to evaluate the effectiveness of individual weather forecasts. The paper evaluates six distinct weather forecasts four different streaming configurations including TCP and UDP streaming, and single and multiple-level encoded videos. The results show that the wireless Received Signal Strength Indicator (RSSI) and average wireless link capacity are the most accurate indicators to predict the performance of streaming video over wireless LANs. The weather forecast philosophy can be beneficial for adapting video streaming in wireless LAN environments.
879315
Kolmogorov Random Graphs and the Incompressibility Method
We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are (i) the mean and variance of the number of (possibly overlapping) ordered labeled subgraphs of a labeled graph as a function of its randomness deficiency (how far it falls short of the maximum possible Kolmogorov complexity) and (ii) a new elementary proof for the number of unlabeled graphs.
40144651
On the Approximation of Shortest Common Supersequences and Longest Common Subsequences
The problems of finding shortest common supersequences (SCS) and longest common subsequences (LCS) are two well-known {\bf NP}-hard problems that have applications in many areas including computational molecular biology, data compression, robot motion planning and scheduling, text editing, etc. A lot of fruitless effort has been spent in searching for good approximation algorithms for these problems. In this paper, we show that these problems are inherently hard to approximate in the worst case. In particular, we prove that (i) SCS does not have a polynomial time linear approximation algorithm, unless {\bf P} = {\bf NP}; (ii) There exists a constant $\delta > 0$ such that, if SCS has a polynomial time approximation algorithm with ratio $\log^{\delta} n$, where $n$ is the number of input sequences, then {\bf NP} is contained in {\bf DTIME}$(2^{\polylog n})$; (iii) There exists a constant $\delta > 0$ such that, if LCS has a polynomial time approximation algorithm with performance ratio $n^{\delta}$, then {\bf P} = {\bf NP}. The proofs utilize the recent results of Arora et al. [Proc. 23rd IEEE Symposium on Foundations of Computer Science, 1992, pp. 14-23] on the complexity of approximation problems. 
In the second part of the paper, we introduce a new method for analyzing the average-case performance of algorithms for sequences, based on Kolmogorov complexity. Despite the above nonapproximability results, we show that near optimal solutions for both SCS and LCS can be found on the average. More precisely, consider a fixed alphabet $\Sigma$ and suppose that the input sequences are generated randomly according to the uniform probability distribution and are of the same length $n$. Moreover, assume that the number of input sequences is polynomial in $n$. Then, there are simple greedy algorithms which approximate SCS and LCS with expected additive errors $O(n^{0.707})$ and $O(n^{\frac{1}{2}+\epsilon})$ for any $\epsilon > 0$, respectively. 
Incidentally, our analyses also provide tight upper and lower bounds on the expected LCS and SCS lengths for a set of random sequences, solving a generalization of another well-known open question on the expected LCS length for two random sequences [K. Alexander, The rate of convergence of the mean length of the longest common subsequence, 1992, manuscript],[V. Chvatal and D. Sankoff, J. Appl. Probab., 12 (1975), pp. 306-315], [D. Sankoff and J. Kruskall, eds., Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison, Addison-Wesley, Reading, MA, 1983].
34458462
Learning in the Presence of Malicious Errors
In this paper an extension of the distribution-free model of learning introduced by Valiant [Comm. ACM, 27(1984), pp. 1134–1142] that allows the presence of malicious errors in the examples given to a learning algorithm is studied. Such errors are generated by an adversary with unbounded computational power and access to the entire history of the learning algorithm’s computation. Thus, a worst-case model of errors is studied.The results of this research include general methods for bounding the rate of error tolerable by any learning algorithm, efficient algorithms tolerating nontrivial rates of malicious errors, and equivalences between problems of learning with errors and standard combinatorial optimization problems.
19172282
A Separator Theorem for One-Dimensional Graphs Under Linear Mapping
Abstract For integers a , b >0, let G =〈 Z n , E ab 〉, where Z n = {0, 1,…, n −1} and E ab ={( i , j )∣ j =( ai + b ) mod n for i ∈ Z n }. G has a separator of size O( n /√log a n ).