Efficient Video Indexing on the Web: A System that Leverages User Interactions with a Video Player

In this paper, we propose a user-based video indexing method, that automatically generates thumbnails of the most important scenes of an online video stream, by analyzing users' interactions with a web video player. As a test bench to verify our idea we have extended the YouTube video player into the VideoSkip system. In addition, VideoSkip uses a web-database (Google Application Engine) to keep a record of some important parameters, such as the timing of basic user actions (play, pause, skip). Moreover, we implemented an algorithm that selects representative thumbnails. Finally, we populated the system with data from an experiment with nine users. We found that the VideoSkip system indexes video content by leveraging implicit users interactions, such as pause and thirty seconds skip. Our early findings point toward improvements of the web video player and its thumbnail generation technique. The VideSkip system could compliment content-based algorithms, in order to achieve efficient video-indexing in difficult videos, such as lectures or sports.Comment: 9 pages, 3 figures, UCMedia 2010: 2nd International ICST Conference on User Centric Medi

Characterization Of A Class Of Graphs Related To Pairs Of Disjoint Matchings

For a given graph consider a pair of disjoint matchings the union of which contains as many edges as possible. Furthermore, consider the relation of the cardinalities of a maximum matching and the largest matching in those pairs. It is known that this relation does not exceed 5/4 for any graph. We characterize the class of graphs for which this relation is precisely 5/4. Our characterization implies that these graphs contain a spanning subgraph, every component of which is the minimal graph of this class.Comment: 33 pages, 10 figure

Spectral transform simulations of finite amplitude double-diffusive instabilities in two dimensions

Simulations of double-diffusion with a two-dimensional, vertical plane spectral transform model reveal details of finite amplitude behavior in salt finger, interleaving and diffusive instabilities. Within the range of fluid parameters studied (3 \u3c σ \u3c 10, .1 \u3c r \u3c .5), infinite, fastest-growing fingers are unstable to Holyer\u27s (1984) nonoscillatory instability and are completely disrupted by it. Finite fingers localized on density steps are also disrupted. Initialized density steps are eroded (the gradients reduced). Fluxes and other diagnostic quantities were determined for salt finger fields at statistical stationarity. These fields contain transitory, irregular finger structures. Fluxes decline steeply as Rfp increases. A single point of comparison of buoyancy flux with ocean measurement yielded good agreement. The dependence of flux ratio on the stability parameter is similar to the linear theory prediction for fastest-growing, infinite fingers and does not increase as Rfp approaches 1, in contrast to laboratory measurements. Holyer\u27s (1984) Floquet theory is extended to the case of nonzero, density compensating, horizontal gradients, and, together with the simulation results, encourages the interpretation of the interleaving instability as being sloping salt fingers. A few preliminary simulations of the diffusive regime indicate very complex behavior. A growing oscillatory perturbation can lead to subcritical convective instability. Such motions sharpen initialized density steps. In the presence of a step, unstable motions are supported even when the fluid is linearly stable to both convection and the diffusive mode

Comparative Study of Two Recent Edge-Detection Algorithms Designed to Process Sea-Surface Temperature Fields

Two algorithms used for the detection of fronts in satellite-derived sea-surface temperature fields are compared. The two algorithms produced surprisingly comparable results considering the substantial differences in the two approaches: multilevel (Algorithm 1) versus locally based (Algorithm 2). Algorithm 1 offers the advantage of shorter run times. Algorithm 2 can be made faster if one is willing to accept less reliable edge detection. Algorithm 1 also offers the advantage of being adaptive and therefore automatic in its application to different data sets. However, when direct control with regard to detection of the edges is demanded, Algorithm 2 contains two tunable parameters to select the smoothness and the strength of edges, while Algorithm 1 as presently coded does not

Approximately coloring graphs without long induced paths

It is an open problem whether the 3-coloring problem can be solved in polynomial time in the class of graphs that do not contain an induced path on $t$ vertices, for fixed $t$. We propose an algorithm that, given a 3-colorable graph without an induced path on $t$ vertices, computes a coloring with $\max\{5,2\lceil{\frac{t-1}{2}}\rceil-2\}$ many colors. If the input graph is triangle-free, we only need $\max\{4,\lceil{\frac{t-1}{2}}\rceil+1\}$ many colors. The running time of our algorithm is $O((3^{t-2}+t^2)m+n)$ if the input graph has $n$ vertices and $m$ edges

On upper bounds for parameters related to construction of special maximum matchings

For a graph $G$ let $L(G)$ and $l(G)$ denote the size of the largest and smallest maximum matching of a graph obtained from $G$ by removing a maximum matching of $G$. We show that $L(G)\leq 2l(G),$ and $L(G)\leq (3/2)l(G)$ provided that $G$ contains a perfect matching. We also characterize the class of graphs for which $L(G)=2l(G)$. Our characterization implies the existence of a polynomial algorithm for testing the property $L(G)=2l(G)$. Finally we show that it is $NP$-complete to test whether a graph $G$ containing a perfect matching satisfies $L(G)=(3/2)l(G)$.Comment: 11 pages, no figure

On disjoint matchings in cubic graphs

For $i=2,3$ and a cubic graph $G$ let $\nu_{i}(G)$ denote the maximum number of edges that can be covered by $i$ matchings. We show that $\nu_{2}(G)\geq {4/5}| V(G)|$ and $\nu_{3}(G)\geq {7/6}| V(G)|$. Moreover, it turns out that $\nu_{2}(G)\leq \frac{|V(G)|+2\nu_{3}(G)}{4}$.Comment: 41 pages, 8 figures, minor chage

On the structure of (pan, even hole)-free graphs

A hole is a chordless cycle with at least four vertices. A pan is a graph which consists of a hole and a single vertex with precisely one neighbor on the hole. An even hole is a hole with an even number of vertices. We prove that a (pan, even hole)-free graph can be decomposed by clique cutsets into essentially unit circular-arc graphs. This structure theorem is the basis of our $O(nm)$-time certifying algorithm for recognizing (pan, even hole)-free graphs and for our $O(n^{2.5}+nm)$-time algorithm to optimally color them. Using this structure theorem, we show that the tree-width of a (pan, even hole)-free graph is at most 1.5 times the clique number minus 1, and thus the chromatic number is at most 1.5 times the clique number.Comment: Accepted to appear in the Journal of Graph Theor

Complexity of Coloring Graphs without Paths and Cycles

Let $P_t$ and $C_\ell$ denote a path on $t$ vertices and a cycle on $\ell$ vertices, respectively. In this paper we study the $k$-coloring problem for $(P_t,C_\ell)$-free graphs. Maffray and Morel, and Bruce, Hoang and Sawada, have proved that 3-colorability of $P_5$-free graphs has a finite forbidden induced subgraphs characterization, while Hoang, Moore, Recoskie, Sawada, and Vatshelle have shown that $k$-colorability of $P_5$-free graphs for $k \geq 4$ does not. These authors have also shown, aided by a computer search, that 4-colorability of $(P_5,C_5)$-free graphs does have a finite forbidden induced subgraph characterization. We prove that for any $k$, the $k$-colorability of $(P_6,C_4)$-free graphs has a finite forbidden induced subgraph characterization. We provide the full lists of forbidden induced subgraphs for $k=3$ and $k=4$. As an application, we obtain certifying polynomial time algorithms for 3-coloring and 4-coloring $(P_6,C_4)$-free graphs. (Polynomial time algorithms have been previously obtained by Golovach, Paulusma, and Song, but those algorithms are not certifying); To complement these results we show that in most other cases the $k$-coloring problem for $(P_t,C_\ell)$-free graphs is NP-complete. Specifically, for $\ell=5$ we show that $k$-coloring is NP-complete for $(P_t,C_5)$-free graphs when $k \ge 4$ and $t \ge 7$; for $\ell \ge 6$ we show that $k$-coloring is NP-complete for $(P_t,C_\ell)$-free graphs when $k \ge 5$, $t \ge 6$; and additionally, for $\ell=7$, we show that $k$-coloring is also NP-complete for $(P_t,C_7)$-free graphs if $k = 4$ and $t\ge 9$. This is the first systematic study of the complexity of the $k$-coloring problem for $(P_t,C_\ell)$-free graphs. We almost completely classify the complexity for the cases when $k \geq 4, \ell \geq 4$, and identify the last three open cases