149 research outputs found
Temporalizing digraphs via linear-size balanced bi-trees
In a directed graph on vertex set , a \emph{forward arc}
is an arc where . A pair is \emph{forward connected} if
there is a directed path from to consisting of forward arcs. In the
{\tt Forward Connected Pairs Problem} ({\tt FCPP}), the input is a strongly
connected digraph , and the output is the maximum number of forward
connected pairs in some vertex enumeration of . We show that {\tt FCPP} is
in APX, as one can efficiently enumerate the vertices of in order to
achieve a quadratic number of forward connected pairs. For this, we construct a
linear size balanced bi-tree (an out-tree and an in-tree with same size
which roots are identified). The existence of such a was left as an open
problem motivated by the study of temporal paths in temporal networks. More
precisely, can be constructed in quadratic time (in the number of vertices)
and has size at least . The algorithm involves a particular depth-first
search tree (Left-DFS) of independent interest, and shows that every strongly
connected directed graph has a balanced separator which is a circuit.
Remarkably, in the request version {\tt RFCPP} of {\tt FCPP}, where the input
is a strong digraph and a set of requests consisting of pairs
, there is no constant such that one can always find an
enumeration realizing forward connected pairs (in either
direction).Comment: 11 pages, 2 figur
On inefficiently connecting temporal networks
A temporal graph can be represented by a graph with an edge labelling, such
that an edge is present in the network if and only if the edge is assigned the
corresponding time label. A journey is a labelled path in a temporal graph such
that labels on successive edges of the path are increasing, and if all vertices
admit journeys to all other vertices, the temporal graph is temporally
connected. A temporal spanner is a sublabelling of the temporal graph such that
temporal connectivity is maintained. The study of temporal spanners has raised
interest since the early 2000's. Essentially two types of studies have been
conducted: the positive side where families of temporal graphs are shown to
(deterministically or stochastically) admit sparse temporal spanners, and the
negative side where constructions of temporal graphs with no sparse spanners
are of importance. Often such studies considered temporal graphs with happy or
simple labellings, which associate exactly one label per edge. In this paper,
we focus on the negative side and consider proper labellings, where multiple
labels per edge are allowed. More precisely, we aim to construct dense
temporally connected graphs such that all labels are necessary for temporal
connectivity. Our contributions are multiple: we present the first labellings
maximizing a local density measure; exact or asymptotically tight results for
basic graph families, which are then extended to larger graph families; an
extension of an efficient temporal graph labelling generator; and overall
denser labellings than previous work even when restricted to happy labellings
Efficient Algorithms for Moral Lineage Tracing
Lineage tracing, the joint segmentation and tracking of living cells as they
move and divide in a sequence of light microscopy images, is a challenging
task. Jug et al. have proposed a mathematical abstraction of this task, the
moral lineage tracing problem (MLTP), whose feasible solutions define both a
segmentation of every image and a lineage forest of cells. Their branch-and-cut
algorithm, however, is prone to many cuts and slow convergence for large
instances. To address this problem, we make three contributions: (i) we devise
the first efficient primal feasible local search algorithms for the MLTP, (ii)
we improve the branch-and-cut algorithm by separating tighter cutting planes
and by incorporating our primal algorithms, (iii) we show in experiments that
our algorithms find accurate solutions on the problem instances of Jug et al.
and scale to larger instances, leveraging moral lineage tracing to practical
significance.Comment: Accepted at ICCV 201
Reconfiguration of Time-Respecting Arborescences
An arborescence, which is a directed analogue of a spanning tree in an
undirected graph, is one of the most fundamental combinatorial objects in a
digraph. In this paper, we study arborescences in digraphs from the viewpoint
of combinatorial reconfiguration, which is the field where we study
reachability between two configurations of some combinatorial objects via some
specified operations. Especially, we consider reconfiguration problems for
time-respecting arborescences, which were introduced by Kempe, Kleinberg, and
Kumar. We first prove that if the roots of the initial and target
time-respecting arborescences are the same, then the target arborescence is
always reachable from the initial one and we can find a shortest
reconfiguration sequence in polynomial time. Furthermore, we show if the roots
are not the same, then the target arborescence may not be reachable from the
initial one. On the other hand, we show that we can determine whether the
target arborescence is reachable form the initial one in polynomial time.
Finally, we prove that it is NP-hard to find a shortest reconfiguration
sequence in the case where the roots are not the same. Our results show an
interesting contrast to the previous results for (ordinary) arborescences
reconfiguration problems.Comment: 13 pages, 3 figures, WADS 202
As Time Goes By: Adding a Temporal Dimension Towards Resolving Delegations in Liquid Democracy
In recent years, the study of various models and questions related to Liquid
Democracy has been of growing interest among the community of Computational
Social Choice. A concern that has been raised, is that current academic
literature focuses solely on static inputs, concealing a key characteristic of
Liquid Democracy: the right for a voter to change her mind as time goes by,
regarding her options of whether to vote herself or delegate her vote to other
participants, till the final voting deadline. In real life, a period of
extended deliberation preceding the election-day motivates voters to adapt
their behaviour over time, either based on observations of the remaining
electorate or on information acquired for the topic at hand. By adding a
temporal dimension to Liquid Democracy, such adaptations can increase the
number of possible delegation paths and reduce the loss of votes due to
delegation cycles or delegating paths towards abstaining agents, ultimately
enhancing participation. Our work takes a first step to integrate a time
horizon into decision-making problems in Liquid Democracy systems. Our
approach, via a computational complexity analysis, exploits concepts and tools
from temporal graph theory which turn out to be convenient for our framework
Detection and Isolation of Link Failures under the Agreement Protocol
In this paper a property of the multi-agent consensus dynamics that relates
the failure of links in the network to jump discontinuities in the derivatives
of the output responses of the nodes is derived and verified analytically. At
the next step, an algorithm for sensor placement is proposed, which would
enable the designer to detect and isolate any link failures across the network
based on the observed jump discontinuities in the derivatives of the responses
of a subset of nodes. These results are explained through elaborative examples.Comment: 6 pages, 3 figures, IEEE Conference on Decision and Control, 201
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