65,002 research outputs found
Dynamic Approximate All-Pairs Shortest Paths: Breaking the O(mn) Barrier and Derandomization
We study dynamic -approximation algorithms for the all-pairs
shortest paths problem in unweighted undirected -node -edge graphs under
edge deletions. The fastest algorithm for this problem is a randomized
algorithm with a total update time of and constant
query time by Roditty and Zwick [FOCS 2004]. The fastest deterministic
algorithm is from a 1981 paper by Even and Shiloach [JACM 1981]; it has a total
update time of and constant query time. We improve these results as
follows: (1) We present an algorithm with a total update time of and constant query time that has an additive error of
in addition to the multiplicative error. This beats the previous
time when . Note that the additive
error is unavoidable since, even in the static case, an -time
(a so-called truly subcubic) combinatorial algorithm with
multiplicative error cannot have an additive error less than ,
unless we make a major breakthrough for Boolean matrix multiplication [Dor et
al. FOCS 1996] and many other long-standing problems [Vassilevska Williams and
Williams FOCS 2010]. The algorithm can also be turned into a
-approximation algorithm (without an additive error) with the
same time guarantees, improving the recent -approximation
algorithm with running
time of Bernstein and Roditty [SODA 2011] in terms of both approximation and
time guarantees. (2) We present a deterministic algorithm with a total update
time of and a query time of . The
algorithm has a multiplicative error of and gives the first
improved deterministic algorithm since 1981. It also answers an open question
raised by Bernstein [STOC 2013].Comment: A preliminary version was presented at the 2013 IEEE 54th Annual
Symposium on Foundations of Computer Science (FOCS 2013
Constraint-Based Heuristic On-line Test Generation from Non-deterministic I/O EFSMs
We are investigating on-line model-based test generation from
non-deterministic output-observable Input/Output Extended Finite State Machine
(I/O EFSM) models of Systems Under Test (SUTs). We propose a novel
constraint-based heuristic approach (Heuristic Reactive Planning Tester (xRPT))
for on-line conformance testing non-deterministic SUTs. An indicative feature
of xRPT is the capability of making reasonable decisions for achieving the test
goals in the on-line testing process by using the results of off-line bounded
static reachability analysis based on the SUT model and test goal
specification. We present xRPT in detail and make performance comparison with
other existing search strategies and approaches on examples with varying
complexity.Comment: In Proceedings MBT 2012, arXiv:1202.582
New Bounds for Randomized List Update in the Paid Exchange Model
We study the fundamental list update problem in the paid exchange model P^d. This cost model was introduced by Manasse, McGeoch and Sleator [M.S. Manasse et al., 1988] and Reingold, Westbrook and Sleator [N. Reingold et al., 1994]. Here the given list of items may only be rearranged using paid exchanges; each swap of two adjacent items in the list incurs a cost of d. Free exchanges of items are not allowed. The model is motivated by the fact that, when executing search operations on a data structure, key comparisons are less expensive than item swaps.
We develop a new randomized online algorithm that achieves an improved competitive ratio against oblivious adversaries. For large d, the competitiveness tends to 2.2442. Technically, the analysis of the algorithm relies on a new approach of partitioning request sequences and charging expected cost. Furthermore, we devise lower bounds on the competitiveness of randomized algorithms against oblivious adversaries. No such lower bounds were known before. Specifically, we prove that no randomized online algorithm can achieve a competitive ratio smaller than 2 in the partial cost model, where an access to the i-th item in the current list incurs a cost of i-1 rather than i. All algorithms proposed in the literature attain their competitiveness in the partial cost model. Furthermore, we show that no randomized online algorithm can achieve a competitive ratio smaller than 1.8654 in the standard full cost model. Again the lower bounds hold for large d
Optimal Lower Bounds for Projective List Update Algorithms
The list update problem is a classical online problem, with an optimal
competitive ratio that is still open, known to be somewhere between 1.5 and
1.6. An algorithm with competitive ratio 1.6, the smallest known to date, is
COMB, a randomized combination of BIT and the TIMESTAMP algorithm TS. This and
almost all other list update algorithms, like MTF, are projective in the sense
that they can be defined by looking only at any pair of list items at a time.
Projectivity (also known as "list factoring") simplifies both the description
of the algorithm and its analysis, and so far seems to be the only way to
define a good online algorithm for lists of arbitrary length. In this paper we
characterize all projective list update algorithms and show that their
competitive ratio is never smaller than 1.6 in the partial cost model.
Therefore, COMB is a best possible projective algorithm in this model.Comment: Version 3 same as version 2, but date in LaTeX \today macro replaced
by March 8, 201
On the List Update Problem with Advice
We study the online list update problem under the advice model of
computation. Under this model, an online algorithm receives partial information
about the unknown parts of the input in the form of some bits of advice
generated by a benevolent offline oracle. We show that advice of linear size is
required and sufficient for a deterministic algorithm to achieve an optimal
solution or even a competitive ratio better than . On the other hand, we
show that surprisingly two bits of advice are sufficient to break the lower
bound of on the competitive ratio of deterministic online algorithms and
achieve a deterministic algorithm with a competitive ratio of . In this
upper-bound argument, the bits of advice determine the algorithm with smaller
cost among three classical online algorithms, TIMESTAMP and two members of the
MTF2 family of algorithms. We also show that MTF2 algorithms are
-competitive
Dynamic Algorithms for the Massively Parallel Computation Model
The Massive Parallel Computing (MPC) model gained popularity during the last
decade and it is now seen as the standard model for processing large scale
data. One significant shortcoming of the model is that it assumes to work on
static datasets while, in practice, real-world datasets evolve continuously. To
overcome this issue, in this paper we initiate the study of dynamic algorithms
in the MPC model.
We first discuss the main requirements for a dynamic parallel model and we
show how to adapt the classic MPC model to capture them. Then we analyze the
connection between classic dynamic algorithms and dynamic algorithms in the MPC
model. Finally, we provide new efficient dynamic MPC algorithms for a variety
of fundamental graph problems, including connectivity, minimum spanning tree
and matching.Comment: Accepted to the 31st ACM Symposium on Parallelism in Algorithms and
Architectures (SPAA 2019
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