129,433 research outputs found
Parameterized temporal exploration problems
In this paper we study the fixed-parameter tractability of the problem of deciding whether a given temporal graph G admits a temporal walk that visits all vertices (temporal exploration) or, in some problem variants, a certain subset of the vertices. Formally, a temporal graph is a sequence G = hG1, . . . , GLi of graphs with V (Gt) = V (G) and E(Gt) ⊆ E(G) for all t ∈ [L] and some underlying graph G, and a temporal walk is a timerespecting sequence of edge-traversals. We consider both the strict variant, in which edges must be traversed in strictly increasing timesteps, and the non-strict variant, in which an arbitrary number of edges can be traversed in each timestep. For both variants, we give FPT algorithms for the problem of finding a temporal walk that visits a given set X of vertices, parameterized by |X|, and for the problem of finding a temporal walk that visits at least k distinct vertices in V (G), parameterized by k. We also show W[2]-hardness for a set version of the temporal exploration problem for both variants. For the non-strict variant, we give an FPT algorithm for the temporal exploration problem parameterized by the lifetime of the input graph, and we show that the temporal exploration problem can be solved in polynomial time if the graph in each timestep has at most two connected components
On the Size and the Approximability of Minimum Temporally Connected Subgraphs
We consider temporal graphs with discrete time labels and investigate the
size and the approximability of minimum temporally connected spanning
subgraphs. We present a family of minimally connected temporal graphs with
vertices and edges, thus resolving an open question of (Kempe,
Kleinberg, Kumar, JCSS 64, 2002) about the existence of sparse temporal
connectivity certificates. Next, we consider the problem of computing a minimum
weight subset of temporal edges that preserve connectivity of a given temporal
graph either from a given vertex r (r-MTC problem) or among all vertex pairs
(MTC problem). We show that the approximability of r-MTC is closely related to
the approximability of Directed Steiner Tree and that r-MTC can be solved in
polynomial time if the underlying graph has bounded treewidth. We also show
that the best approximation ratio for MTC is at least and at most , for
any constant , where is the number of temporal edges and
is the maximum degree of the underlying graph. Furthermore, we prove
that the unweighted version of MTC is APX-hard and that MTC is efficiently
solvable in trees and -approximable in cycles
Attribute Exploration of Discrete Temporal Transitions
Discrete temporal transitions occur in a variety of domains, but this work is
mainly motivated by applications in molecular biology: explaining and analyzing
observed transcriptome and proteome time series by literature and database
knowledge. The starting point of a formal concept analysis model is presented.
The objects of a formal context are states of the interesting entities, and the
attributes are the variable properties defining the current state (e.g.
observed presence or absence of proteins). Temporal transitions assign a
relation to the objects, defined by deterministic or non-deterministic
transition rules between sets of pre- and postconditions. This relation can be
generalized to its transitive closure, i.e. states are related if one results
from the other by a transition sequence of arbitrary length. The focus of the
work is the adaptation of the attribute exploration algorithm to such a
relational context, so that questions concerning temporal dependencies can be
asked during the exploration process and be answered from the computed stem
base. Results are given for the abstract example of a game and a small gene
regulatory network relevant to a biomedical question.Comment: Only the email address and reference have been replace
Real-Time Synthesis is Hard!
We study the reactive synthesis problem (RS) for specifications given in
Metric Interval Temporal Logic (MITL). RS is known to be undecidable in a very
general setting, but on infinite words only; and only the very restrictive BRRS
subcase is known to be decidable (see D'Souza et al. and Bouyer et al.). In
this paper, we precise the decidability border of MITL synthesis. We show RS is
undecidable on finite words too, and present a landscape of restrictions (both
on the logic and on the possible controllers) that are still undecidable. On
the positive side, we revisit BRRS and introduce an efficient on-the-fly
algorithm to solve it
Parallel symbolic state-space exploration is difficult, but what is the alternative?
State-space exploration is an essential step in many modeling and analysis
problems. Its goal is to find the states reachable from the initial state of a
discrete-state model described. The state space can used to answer important
questions, e.g., "Is there a dead state?" and "Can N become negative?", or as a
starting point for sophisticated investigations expressed in temporal logic.
Unfortunately, the state space is often so large that ordinary explicit data
structures and sequential algorithms cannot cope, prompting the exploration of
(1) parallel approaches using multiple processors, from simple workstation
networks to shared-memory supercomputers, to satisfy large memory and runtime
requirements and (2) symbolic approaches using decision diagrams to encode the
large structured sets and relations manipulated during state-space generation.
Both approaches have merits and limitations. Parallel explicit state-space
generation is challenging, but almost linear speedup can be achieved; however,
the analysis is ultimately limited by the memory and processors available.
Symbolic methods are a heuristic that can efficiently encode many, but not all,
functions over a structured and exponentially large domain; here the pitfalls
are subtler: their performance varies widely depending on the class of decision
diagram chosen, the state variable order, and obscure algorithmic parameters.
As symbolic approaches are often much more efficient than explicit ones for
many practical models, we argue for the need to parallelize symbolic
state-space generation algorithms, so that we can realize the advantage of both
approaches. This is a challenging endeavor, as the most efficient symbolic
algorithm, Saturation, is inherently sequential. We conclude by discussing
challenges, efforts, and promising directions toward this goal
Shortest, Fastest, and Foremost Broadcast in Dynamic Networks
Highly dynamic networks rarely offer end-to-end connectivity at a given time.
Yet, connectivity in these networks can be established over time and space,
based on temporal analogues of multi-hop paths (also called {\em journeys}).
Attempting to optimize the selection of the journeys in these networks
naturally leads to the study of three cases: shortest (minimum hop), fastest
(minimum duration), and foremost (earliest arrival) journeys. Efficient
centralized algorithms exists to compute all cases, when the full knowledge of
the network evolution is given.
In this paper, we study the {\em distributed} counterparts of these problems,
i.e. shortest, fastest, and foremost broadcast with termination detection
(TDB), with minimal knowledge on the topology.
We show that the feasibility of each of these problems requires distinct
features on the evolution, through identifying three classes of dynamic graphs
wherein the problems become gradually feasible: graphs in which the
re-appearance of edges is {\em recurrent} (class R), {\em bounded-recurrent}
(B), or {\em periodic} (P), together with specific knowledge that are
respectively (the number of nodes), (a bound on the recurrence
time), and (the period). In these classes it is not required that all pairs
of nodes get in contact -- only that the overall {\em footprint} of the graph
is connected over time.
Our results, together with the strict inclusion between , , and ,
implies a feasibility order among the three variants of the problem, i.e.
TDB[foremost] requires weaker assumptions on the topology dynamics than
TDB[shortest], which itself requires less than TDB[fastest]. Reversely, these
differences in feasibility imply that the computational powers of ,
, and also form a strict hierarchy
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