513 research outputs found

### Scheduling Packets with Values and Deadlines in Size-bounded Buffers

Motivated by providing quality-of-service differentiated services in the
Internet, we consider buffer management algorithms for network switches. We
study a multi-buffer model. A network switch consists of multiple size-bounded
buffers such that at any time, the number of packets residing in each
individual buffer cannot exceed its capacity. Packets arrive at the network
switch over time; they have values, deadlines, and designated buffers. In each
time step, at most one pending packet is allowed to be sent and this packet can
be from any buffer. The objective is to maximize the total value of the packets
sent by their respective deadlines. A 9.82-competitive online algorithm has
been provided for this model (Azar and Levy. SWAT 2006), but no offline
algorithms have been known yet. In this paper, We study the offline setting of
the multi-buffer model. Our contributions include a few optimal offline
algorithms for some variants of the model. Each variant has its unique and
interesting algorithmic feature. These offline algorithms help us understand
the model better in designing online algorithms.Comment: 7 page

### Exact bounds for distributed graph colouring

We prove exact bounds on the time complexity of distributed graph colouring.
If we are given a directed path that is properly coloured with $n$ colours, by
prior work it is known that we can find a proper 3-colouring in $\frac{1}{2}
\log^*(n) \pm O(1)$ communication rounds. We close the gap between upper and
lower bounds: we show that for infinitely many $n$ the time complexity is
precisely $\frac{1}{2} \log^* n$ communication rounds.Comment: 16 pages, 3 figure

### The Irreducible Spine(s) of Undirected Networks

Using closure concepts, we show that within every undirected network, or
graph, there is a unique irreducible subgraph which we call its "spine". The
chordless cycles which comprise this irreducible core effectively characterize
the connectivity structure of the network as a whole. In particular, it is
shown that the center of the network, whether defined by distance or
betweenness centrality, is effectively contained in this spine. By counting the
number of cycles of length 3 <= k <= max_length, we can also create a kind of
signature that can be used to identify the network. Performance is analyzed,
and the concepts we develop are illurstrated by means of a relatively small
running sample network of about 400 nodes.Comment: Submitted to WISE 201

### A simpler and more efficient algorithm for the next-to-shortest path problem

Given an undirected graph $G=(V,E)$ with positive edge lengths and two
vertices $s$ and $t$, the next-to-shortest path problem is to find an $st$-path
which length is minimum amongst all $st$-paths strictly longer than the
shortest path length. In this paper we show that the problem can be solved in
linear time if the distances from $s$ and $t$ to all other vertices are given.
Particularly our new algorithm runs in $O(|V|\log |V|+|E|)$ time for general
graphs, which improves the previous result of $O(|V|^2)$ time for sparse
graphs, and takes only linear time for unweighted graphs, planar graphs, and
graphs with positive integer edge lengths.Comment: Partial result appeared in COCOA201

### Unbiased taxonomic annotation of metagenomic samples

The classification of reads from a metagenomic sample using a reference taxonomy is usually based on first mapping the reads to the reference sequences and then classifying each read at a node under the lowest common ancestor of the candidate sequences in the reference taxonomy with the least classification error. However, this taxonomic annotation can be biased by an imbalanced taxonomy and also by the presence of multiple nodes in the taxonomy with the least classification error for a given read. In this article, we show that the Rand index is a better indicator of classification error than the often used area under thereceiver operating characteristic (ROC) curve andF-measure for both balanced and imbalanced reference taxonomies, and we also address the second source of bias by reducing the taxonomic annotation problem for a whole metagenomic sample to a set cover problem, for which a logarithmic approximation can be obtained in linear time and an exact solution can be obtained by integer linear programming. Experimental results with a proof-of-concept implementation of the set cover approach to taxonomic annotation in a next release of the TANGO software show that the set cover approach further reduces ambiguity in the taxonomic annotation obtained with TANGO without distorting the relative abundance profile of the metagenomic sample.Peer ReviewedPostprint (published version

### Undirected Graphs of Entanglement Two

Entanglement is a complexity measure of directed graphs that origins in fixed
point theory. This measure has shown its use in designing efficient algorithms
to verify logical properties of transition systems. We are interested in the
problem of deciding whether a graph has entanglement at most k. As this measure
is defined by means of games, game theoretic ideas naturally lead to design
polynomial algorithms that, for fixed k, decide the problem. Known
characterizations of directed graphs of entanglement at most 1 lead, for k = 1,
to design even faster algorithms. In this paper we present an explicit
characterization of undirected graphs of entanglement at most 2. With such a
characterization at hand, we devise a linear time algorithm to decide whether
an undirected graph has this property

### Frameworks for logically classifying polynomial-time optimisation problems.

We show that a logical framework, based around a fragment of existential second-order logic formerly proposed by others so as to capture the class of polynomially-bounded P-optimisation problems, cannot hope to do so, under the assumption that P ≠ NP. We do this by exhibiting polynomially-bounded maximisation and minimisation problems that can be expressed in the framework but whose decision versions are NP-complete. We propose an alternative logical framework, based around inflationary fixed-point logic, and show that we can capture the above classes of optimisation problems. We use the inductive depth of an inflationary fixed-point as a means to describe the objective functions of the instances of our optimisation problems

### Scaling in a continuous time model for biological aging

In this paper we consider a generalization to the asexual version of the
Penna model for biological aging, where we take a continuous time limit. The
genotype associated to each individual is an interval of real numbers over
which Dirac $\delta$--functions are defined, representing genetically
programmed diseases to be switched on at defined ages of the individual life.
We discuss two different continuous limits for the evolution equation and two
different mutation protocols, to be implemented during reproduction. Exact
stationary solutions are obtained and scaling properties are discussed.Comment: 10 pages, 6 figure

### Selection from read-only memory with limited workspace

Given an unordered array of $N$ elements drawn from a totally ordered set and
an integer $k$ in the range from $1$ to $N$, in the classic selection problem
the task is to find the $k$-th smallest element in the array. We study the
complexity of this problem in the space-restricted random-access model: The
input array is stored on read-only memory, and the algorithm has access to a
limited amount of workspace. We prove that the linear-time prune-and-search
algorithm---presented in most textbooks on algorithms---can be modified to use
$\Theta(N)$ bits instead of $\Theta(N)$ words of extra space. Prior to our
work, the best known algorithm by Frederickson could perform the task with
$\Theta(N)$ bits of extra space in $O(N \lg^{*} N)$ time. Our result separates
the space-restricted random-access model and the multi-pass streaming model,
since we can surpass the $\Omega(N \lg^{*} N)$ lower bound known for the latter
model. We also generalize our algorithm for the case when the size of the
workspace is $\Theta(S)$ bits, where $\lg^3{N} \leq S \leq N$. The running time
of our generalized algorithm is $O(N \lg^{*}(N/S) + N (\lg N) / \lg{} S)$,
slightly improving over the $O(N \lg^{*}(N (\lg N)/S) + N (\lg N) / \lg{} S)$
bound of Frederickson's algorithm. To obtain the improvements mentioned above,
we developed a new data structure, called the wavelet stack, that we use for
repeated pruning. We expect the wavelet stack to be a useful tool in other
applications as well.Comment: 16 pages, 1 figure, Preliminary version appeared in COCOON-201

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