12,793 research outputs found
An Efficient Local Search for Partial Latin Square Extension Problem
A partial Latin square (PLS) is a partial assignment of n symbols to an nxn
grid such that, in each row and in each column, each symbol appears at most
once. The partial Latin square extension problem is an NP-hard problem that
asks for a largest extension of a given PLS. In this paper we propose an
efficient local search for this problem. We focus on the local search such that
the neighborhood is defined by (p,q)-swap, i.e., removing exactly p symbols and
then assigning symbols to at most q empty cells. For p in {1,2,3}, our
neighborhood search algorithm finds an improved solution or concludes that no
such solution exists in O(n^{p+1}) time. We also propose a novel swap
operation, Trellis-swap, which is a generalization of (1,q)-swap and
(2,q)-swap. Our Trellis-neighborhood search algorithm takes O(n^{3.5}) time to
do the same thing. Using these neighborhood search algorithms, we design a
prototype iterated local search algorithm and show its effectiveness in
comparison with state-of-the-art optimization solvers such as IBM ILOG CPLEX
and LocalSolver.Comment: 17 pages, 2 figure
Decomposition Based Search - A theoretical and experimental evaluation
In this paper we present and evaluate a search strategy called Decomposition
Based Search (DBS) which is based on two steps: subproblem generation and
subproblem solution. The generation of subproblems is done through value
ranking and domain splitting. Subdomains are explored so as to generate,
according to the heuristic chosen, promising subproblems first.
We show that two well known search strategies, Limited Discrepancy Search
(LDS) and Iterative Broadening (IB), can be seen as special cases of DBS. First
we present a tuning of DBS that visits the same search nodes as IB, but avoids
restarts. Then we compare both theoretically and computationally DBS and LDS
using the same heuristic. We prove that DBS has a higher probability of being
successful than LDS on a comparable number of nodes, under realistic
assumptions. Experiments on a constraint satisfaction problem and an
optimization problem show that DBS is indeed very effective if compared to LDS.Comment: 16 pages, 8 figures. LIA Technical Report LIA00203, University of
Bologna, 200
Postponing Branching Decisions
Solution techniques for Constraint Satisfaction and Optimisation Problems
often make use of backtrack search methods, exploiting variable and value
ordering heuristics. In this paper, we propose and analyse a very simple method
to apply in case the value ordering heuristic produces ties: postponing the
branching decision. To this end, we group together values in a tie, branch on
this sub-domain, and defer the decision among them to lower levels of the
search tree. We show theoretically and experimentally that this simple
modification can dramatically improve the efficiency of the search strategy.
Although in practise similar methods may have been applied already, to our
knowledge, no empirical or theoretical study has been proposed in the
literature to identify when and to what extent this strategy should be used.Comment: 11 pages, 3 figure
Physical Layer Network Coding for Two-Way Relaying with QAM
The design of modulation schemes for the physical layer network-coded two way
relaying scenario was studied in [1], [3], [4] and [5]. In [7] it was shown
that every network coding map that satisfies the exclusive law is representable
by a Latin Square and conversely, and this relationship can be used to get the
network coding maps satisfying the exclusive law. But, only the scenario in
which the end nodes use -PSK signal sets is addressed in [7] and [8]. In
this paper, we address the case in which the end nodes use -QAM signal sets.
In a fading scenario, for certain channel conditions ,
termed singular fade states, the MA phase performance is greatly reduced. By
formulating a procedure for finding the exact number of singular fade states
for QAM, we show that square QAM signal sets give lesser number of singular
fade states compared to PSK signal sets. This results in superior performance
of -QAM over -PSK. It is shown that the criterion for partitioning the
complex plane, for the purpose of using a particular network code for a
particular fade state, is different from that used for -PSK. Using a
modified criterion, we describe a procedure to analytically partition the
complex plane representing the channel condition. We show that when -QAM () signal set is used, the conventional XOR network mapping fails to remove
the ill effects of , which is a singular fade state for
all signal sets of arbitrary size. We show that a doubly block circulant Latin
Square removes this singular fade state for -QAM.Comment: 13 pages, 14 figures, submitted to IEEE Trans. Wireless
Communications. arXiv admin note: substantial text overlap with
arXiv:1203.326
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