11,821 research outputs found
Shortest Paths Avoiding Forbidden Subpaths
In this paper we study a variant of the shortest path problem in graphs:
given a weighted graph G and vertices s and t, and given a set X of forbidden
paths in G, find a shortest s-t path P such that no path in X is a subpath of
P. Path P is allowed to repeat vertices and edges. We call each path in X an
exception, and our desired path a shortest exception-avoiding path. We
formulate a new version of the problem where the algorithm has no a priori
knowledge of X, and finds out about an exception x in X only when a path
containing x fails. This situation arises in computing shortest paths in
optical networks. We give an algorithm that finds a shortest exception avoiding
path in time polynomial in |G| and |X|. The main idea is to run Dijkstra's
algorithm incrementally after replicating vertices when an exception is
discovered.Comment: 12 pages, 2 figures. Fixed a few typos, rephrased a few sentences,
and used the STACS styl
The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs
We study the problem of transforming one list (vertex) coloring of a graph
into another list coloring by changing only one vertex color assignment at a
time, while at all times maintaining a list coloring, given a list of allowed
colors for each vertex. This problem is known to be PSPACE-complete for
bipartite planar graphs. In this paper, we first show that the problem remains
PSPACE-complete even for bipartite series-parallel graphs, which form a proper
subclass of bipartite planar graphs. We note that our reduction indeed shows
the PSPACE-completeness for graphs with pathwidth two, and it can be extended
for threshold graphs. In contrast, we give a polynomial-time algorithm to solve
the problem for graphs with pathwidth one. Thus, this paper gives precise
analyses of the problem with respect to pathwidth
Minimum Input Selection for Structural Controllability
Given a linear system , where is an matrix
with nonzero entries, we consider the problem of finding the smallest set
of state variables to affect with an input so that the resulting system is
structurally controllable. We further assume we are given a set of "forbidden
state variables" which cannot be affected with an input and which we have
to avoid in our selection. Our main result is that this problem can be solved
deterministically in operations
Shortest path and maximum flow problems in planar flow networks with additive gains and losses
In contrast to traditional flow networks, in additive flow networks, to every
edge e is assigned a gain factor g(e) which represents the loss or gain of the
flow while using edge e. Hence, if a flow f(e) enters the edge e and f(e) is
less than the designated capacity of e, then f(e) + g(e) = 0 units of flow
reach the end point of e, provided e is used, i.e., provided f(e) != 0. In this
report we study the maximum flow problem in additive flow networks, which we
prove to be NP-hard even when the underlying graphs of additive flow networks
are planar. We also investigate the shortest path problem, when to every edge e
is assigned a cost value for every unit flow entering edge e, which we show to
be NP-hard in the strong sense even when the additive flow networks are planar
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