2,965 research outputs found
Bisection of Bounded Treewidth Graphs by Convolutions
In the Bisection problem, we are given as input an edge-weighted graph G. The task is to find a partition of V(G) into two parts A and B such that ||A| - |B|| <= 1 and the sum of the weights of the edges with one endpoint in A and the other in B is minimized. We show that the complexity of the Bisection problem on trees, and more generally on graphs of bounded treewidth, is intimately linked to the (min, +)-Convolution problem. Here the input consists of two sequences (a[i])^{n-1}_{i = 0} and (b[i])^{n-1}_{i = 0}, the task is to compute the sequence (c[i])^{n-1}_{i = 0}, where c[k] = min_{i=0,...,k}(a[i] + b[k - i]).
In particular, we prove that if (min, +)-Convolution can be solved in O(tau(n)) time, then Bisection of graphs of treewidth t can be solved in time O(8^t t^{O(1)} log n * tau(n)), assuming a tree decomposition of width t is provided as input. Plugging in the naive O(n^2) time algorithm for (min, +)-Convolution yields a O(8^t t^{O(1)} n^2 log n) time algorithm for Bisection. This improves over the (dependence on n of the) O(2^t n^3) time algorithm of Jansen et al. [SICOMP 2005] at the cost of a worse dependence on t. "Conversely", we show that if Bisection can be solved in time O(beta(n)) on edge weighted trees, then (min, +)-Convolution can be solved in O(beta(n)) time as well. Thus, obtaining a sub-quadratic algorithm for Bisection on trees is extremely challenging, and could even be impossible. On the other hand, for unweighted graphs of treewidth t, by making use of a recent algorithm for Bounded Difference (min, +)-Convolution of Chan and Lewenstein [STOC 2015], we obtain a sub-quadratic algorithm for Bisection with running time O(8^t t^{O(1)} n^{1.864} log n)
Simultaneous Feedback Vertex Set: A Parameterized Perspective
Given a family of graphs , a graph , and a positive integer
, the -Deletion problem asks whether we can delete at most
vertices from to obtain a graph in . -Deletion
generalizes many classical graph problems such as Vertex Cover, Feedback Vertex
Set, and Odd Cycle Transversal. A graph ,
where the edge set of is partitioned into color classes, is called
an -edge-colored graph. A natural extension of the
-Deletion problem to edge-colored graphs is the
-Simultaneous -Deletion problem. In the latter problem, we
are given an -edge-colored graph and the goal is to find a set
of at most vertices such that each graph , where and , is in . In this work, we
study -Simultaneous -Deletion for being the
family of forests. In other words, we focus on the -Simultaneous
Feedback Vertex Set (-SimFVS) problem. Algorithmically, we show that,
like its classical counterpart, -SimFVS parameterized by is
fixed-parameter tractable (FPT) and admits a polynomial kernel, for any fixed
constant . In particular, we give an algorithm running in time and a kernel with vertices. The
running time of our algorithm implies that -SimFVS is FPT even when
. We complement this positive result by showing that for
, where is the number of vertices in the input graph,
-SimFVS becomes W[1]-hard. Our positive results answer one of the open
problems posed by Cai and Ye (MFCS 2014)
The Effect of Interfacial Chemical Bonding in TiO2-SiO2 Composites on their Photocatalytic NOx Abatement Performance
The authors gratefully acknowledge funding from the UK Engineering and Physical Sciences Research Council (Grant Ref: EP/M003299/1) and the Natural Science Foundation of China (No. 51461135005) International Joint Research Project (EPSRC-NSFC).Peer reviewedPublisher PD
Photocatalyst efficiencies in concrete technology : the effect of photocatalyst placement
The authors gratefully acknowledge funding from the UK Engineering and Physical Sciences Research Council (Grant Ref: EP/M003299/1) and the Natural Science Foundation of China (No. 51461135005, No. 51478370) International Joint Research Project (EPSRC-NSFC).Peer reviewedPublisher PD
Self-Repairing Disk Arrays
As the prices of magnetic storage continue to decrease, the cost of replacing
failed disks becomes increasingly dominated by the cost of the service call
itself. We propose to eliminate these calls by building disk arrays that
contain enough spare disks to operate without any human intervention during
their whole lifetime. To evaluate the feasibility of this approach, we have
simulated the behavior of two-dimensional disk arrays with n parity disks and
n(n-1)/2 data disks under realistic failure and repair assumptions. Our
conclusion is that having n(n+1)/2 spare disks is more than enough to achieve a
99.999 percent probability of not losing data over four years. We observe that
the same objectives cannot be reached with RAID level 6 organizations and would
require RAID stripes that could tolerate triple disk failures.Comment: Part of ADAPT Workshop proceedings, 2015 (arXiv:1412.2347
Implementation of horizontal well CBM/ECBM technology and the assessment of effective CO2 storage capacity in a Scottish coalfield
Acknowledgements The authors wish to thank Composite Energy Ltd., the BG Group, Scottish Power and the Royal Bank of Scotland for their funding and contributions towards the research reported in this paper.Non peer reviewedPublisher PD
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