946 research outputs found
Optimal competitiveness for the Rectilinear Steiner Arborescence problem
We present optimal online algorithms for two related known problems involving
Steiner Arborescence, improving both the lower and the upper bounds. One of
them is the well studied continuous problem of the {\em Rectilinear Steiner
Arborescence} (). We improve the lower bound and the upper bound on the
competitive ratio for from and to
, where is the number of Steiner
points. This separates the competitive ratios of and the Symetric-,
two problems for which the bounds of Berman and Coulston is STOC 1997 were
identical. The second problem is one of the Multimedia Content Distribution
problems presented by Papadimitriou et al. in several papers and Charikar et
al. SODA 1998. It can be viewed as the discrete counterparts (or a network
counterpart) of . For this second problem we present tight bounds also in
terms of the network size, in addition to presenting tight bounds in terms of
the number of Steiner points (the latter are similar to those we derived for
)
Settling Some Open Problems on 2-Player Symmetric Nash Equilibria
Over the years, researchers have studied the complexity of several decision
versions of Nash equilibrium in (symmetric) two-player games (bimatrix games).
To the best of our knowledge, the last remaining open problem of this sort is
the following; it was stated by Papadimitriou in 2007: find a non-symmetric
Nash equilibrium (NE) in a symmetric game. We show that this problem is
NP-complete and the problem of counting the number of non-symmetric NE in a
symmetric game is #P-complete.
In 2005, Kannan and Theobald defined the "rank of a bimatrix game"
represented by matrices (A, B) to be rank(A+B) and asked whether a NE can be
computed in rank 1 games in polynomial time. Observe that the rank 0 case is
precisely the zero sum case, for which a polynomial time algorithm follows from
von Neumann's reduction of such games to linear programming. In 2011, Adsul et.
al. obtained an algorithm for rank 1 games; however, it does not solve the case
of symmetric rank 1 games. We resolve this problem
Euclidean TSP with few inner points in linear space
Given a set of points in the Euclidean plane, such that just points
are strictly inside the convex hull of the whole set, we want to find the
shortest tour visiting every point. The fastest known algorithm for the version
when is significantly smaller than , i.e., when there are just few inner
points, works in time [Knauer and Spillner,
WG 2006], but also requires space of order . The best
linear space algorithm takes time [Deineko, Hoffmann, Okamoto,
Woeginer, Oper. Res. Lett. 34(1), 106-110]. We construct a linear space
time algorithm. The new insight is extending the
known divide-and-conquer method based on planar separators with a
matching-based argument to shrink the instance in every recursive call. This
argument also shows that the problem admits a quadratic bikernel.Comment: under submissio
A PTAS for Bounded-Capacity Vehicle Routing in Planar Graphs
The Capacitated Vehicle Routing problem is to find a minimum-cost set of
tours that collectively cover clients in a graph, such that each tour starts
and ends at a specified depot and is subject to a capacity bound on the number
of clients it can serve. In this paper, we present a polynomial-time
approximation scheme (PTAS) for instances in which the input graph is planar
and the capacity is bounded. Previously, only a quasipolynomial-time
approximation scheme was known for these instances. To obtain this result, we
show how to embed planar graphs into bounded-treewidth graphs while preserving,
in expectation, the client-to-client distances up to a small additive error
proportional to client distances to the depot
An Innovative Approach to Achieve Compositionality Efficiently using Multi-Version Object Based Transactional Systems
In the modern era of multicore processors, utilizing cores is a tedious job.
Synchronization and communication among processors involve high cost. Software
transaction memory systems (STMs) addresses this issues and provide better
concurrency in which programmer need not have to worry about consistency
issues. Another advantage of STMs is that they facilitate compositionality of
concurrent programs with great ease. Different concurrent operations that need
to be composed to form a single atomic unit is achieved by encapsulating them
in a single transaction. In this paper, we introduce a new STM system as
multi-version object based STM (MVOSTM) which is the combination of both of
these ideas for harnessing greater concurrency in STMs. As the name suggests
MVOSTM, works on a higher level and maintains multiple versions corresponding
to each key. We have developed MVOSTM with the unlimited number of versions
corresponding to each key. In addition to that, we have developed garbage
collection for MVOSTM (MVOSTM-GC) to delete unwanted versions corresponding to
the keys to reduce traversal overhead. MVOSTM provides greater concurrency
while reducing the number of aborts and it ensures compositionality by making
the transactions atomic. Here, we have used MVOSTM for the list and hash-table
data structure as list-MVOSTM and HT- MVOSTM. Experimental results of
list-MVOSTM outperform almost two to twenty fold speedup than existing
state-of-the-art list based STMs (Trans-list, Boosting-list, NOrec-list,
list-MVTO, and list-OSTM). HT-MVOSTM shows a significant performance gain of
almost two to nineteen times better than existing state-of-the-art hash-table
based STMs (ESTM, RWSTMs, HT-MVTO, and HT-OSTM). MVOSTM with list and
hash-table shows the least number of aborts among all the existing STM
algorithms. MVOSTM satisfies correctness-criteria as opacity.Comment: 35 pages, 23 figure
Measuring Coverage of Prolog Programs Using Mutation Testing
Testing is an important aspect in professional software development, both to
avoid and identify bugs as well as to increase maintainability. However,
increasing the number of tests beyond a reasonable amount hinders development
progress. To decide on the completeness of a test suite, many approaches to
assert test coverage have been suggested. Yet, frameworks for logic programs
remain scarce.
In this paper, we introduce a framework for Prolog programs measuring test
coverage using mutations. We elaborate the main ideas of mutation testing and
transfer them to logic programs. To do so, we discuss the usefulness of
different mutations in the context of Prolog and empirically evaluate them in a
new mutation testing framework on different examples.Comment: 16 pages, Accepted for presentation in WFLP 201
Stable divisorial gonality is in NP
Divisorial gonality and stable divisorial gonality are graph parameters,
which have an origin in algebraic geometry. Divisorial gonality of a connected
graph can be defined with help of a chip firing game on . The stable
divisorial gonality of is the minimum divisorial gonality over all
subdivisions of edges of .
In this paper we prove that deciding whether a given connected graph has
stable divisorial gonality at most a given integer belongs to the class NP.
Combined with the result that (stable) divisorial gonality is NP-hard by
Gijswijt, we obtain that stable divisorial gonality is NP-complete. The proof
consist of a partial certificate that can be verified by solving an Integer
Linear Programming instance. As a corollary, we have that the number of
subdivisions needed for minimum stable divisorial gonality of a graph with
vertices is bounded by for a polynomial
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