87 research outputs found
Data optimizations for constraint automata
Constraint automata (CA) constitute a coordination model based on finite
automata on infinite words. Originally introduced for modeling of coordinators,
an interesting new application of CAs is implementing coordinators (i.e.,
compiling CAs into executable code). Such an approach guarantees
correctness-by-construction and can even yield code that outperforms
hand-crafted code. The extent to which these two potential advantages
materialize depends on the smartness of CA-compilers and the existence of
proofs of their correctness.
Every transition in a CA is labeled by a "data constraint" that specifies an
atomic data-flow between coordinated processes as a first-order formula. At
run-time, compiler-generated code must handle data constraints as efficiently
as possible. In this paper, we present, and prove the correctness of two
optimization techniques for CA-compilers related to handling of data
constraints: a reduction to eliminate redundant variables and a translation
from (declarative) data constraints to (imperative) data commands expressed in
a small sequential language. Through experiments, we show that these
optimization techniques can have a positive impact on performance of generated
executable code
Design Of A Min-Sum Arborescence With Outage Costs
We present an integer programming formulation of the min-sum arborescence with node outage costs problem. The solution to the problem consists of selecting links to connect a set of terminal nodes to a root node with minimal expected annual cost, where the annual cost is the sum of annual links costs and annual outage costs. The links in the network are prone to failure and each terminal node has an associated outage cost, which is the economic cost incurred by the network user whenever that node is disabled from the central node due to failure of a link. We suggest a Lagrangian-based heuristic to get a good solution to this problem. This solution procedure also gives lower bounds to the optimal solution and is used to assess the quality of the heuristic solution. Numerical experiments taken from instances with up to 100 nodes are used to evaluate the performance of the proposed heuristic
Blocking optimal -arborescences
Given a digraph and a positive integer , an arc set is called a \textbf{-arborescence} if it is the disjoint union of
spanning arborescences. The problem of finding a minimum cost -arborescence
is known to be polynomial-time solvable using matroid intersection. In this
paper we study the following problem: find a minimum cardinality subset of arcs
that contains at least one arc from every minimum cost -arborescence. For
, the problem was solved in [A. Bern\'ath, G. Pap , Blocking optimal
arborescences, IPCO 2013]. In this paper we give an algorithm for general
that has polynomial running time if is fixed
Parameterized complexity of the MINCCA problem on graphs of bounded decomposability
In an edge-colored graph, the cost incurred at a vertex on a path when two
incident edges with different colors are traversed is called reload or
changeover cost. The "Minimum Changeover Cost Arborescence" (MINCCA) problem
consists in finding an arborescence with a given root vertex such that the
total changeover cost of the internal vertices is minimized. It has been
recently proved by G\"oz\"upek et al. [TCS 2016] that the problem is FPT when
parameterized by the treewidth and the maximum degree of the input graph. In
this article we present the following results for the MINCCA problem:
- the problem is W[1]-hard parameterized by the treedepth of the input graph,
even on graphs of average degree at most 8. In particular, it is W[1]-hard
parameterized by the treewidth of the input graph, which answers the main open
problem of G\"oz\"upek et al. [TCS 2016];
- it is W[1]-hard on multigraphs parameterized by the tree-cutwidth of the
input multigraph;
- it is FPT parameterized by the star tree-cutwidth of the input graph, which
is a slightly restricted version of tree-cutwidth. This result strictly
generalizes the FPT result given in G\"oz\"upek et al. [TCS 2016];
- it remains NP-hard on planar graphs even when restricted to instances with
at most 6 colors and 0/1 symmetric costs, or when restricted to instances with
at most 8 colors, maximum degree bounded by 4, and 0/1 symmetric costs.Comment: 25 pages, 11 figure
Global and Fixed-Terminal Cuts in Digraphs
The computational complexity of multicut-like problems may vary significantly depending on whether the terminals are fixed or not. In this work we present a comprehensive study of this phenomenon in two types of cut problems in directed graphs: double cut and bicut.
1. Fixed-terminal edge-weighted double cut is known to be solvable efficiently. We show that fixed-terminal node-weighted double cut cannot be approximated to a factor smaller than 2 under the Unique Games Conjecture (UGC), and we also give a 2-approximation algorithm. For the global version of the problem, we prove an inapproximability bound of 3/2 under UGC.
2. Fixed-terminal edge-weighted bicut is known to have an approximability factor of 2 that is tight under UGC. We show that the global edge-weighted bicut is approximable to
a factor strictly better than 2, and that the global node-weighted bicut cannot be approximated to a factor smaller than 3/2 under UGC.
3. In relation to these investigations, we also prove two results on undirected graphs which are of independent interest. First, we show NP-completeness and a tight inapproximability bound of 4/3 for the node-weighted 3-cut problem under UGC. Second, we show that for constant k, there exists an efficient algorithm to solve the minimum {s,t}-separating k-cut problem.
Our techniques for the algorithms are combinatorial, based on LPs and based on the enumeration of approximate min-cuts. Our hardness results are based on combinatorial reductions and integrality gap instances
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