scholarly journals Lossy Compression of Pattern Databases Using Acyclic Random Hypergraphs

2017 ◽  
Author(s):  
Mehdi Sadeqi ◽  
Howard J. Hamilton
Keyword(s):  
Bloom Filter ◽  
Lookup Table ◽  
Compression Rate ◽  
Memory Space ◽  
Uniform Hypergraphs ◽  
Random Hypergraph ◽  
The Cost ◽  
Random Hypergraphs ◽  
Domain Independent ◽  
Pattern Databases

A domain-independent heuristic function created by an abstraction is usually implemented using a Pattern Database (PDB), which is a lookup table of (abstract state, heuristic value) pairs. PDBs containing high quality heuristic values generally require substantial memory space and therefore need to be compressed. In this paper, we introduce Acyclic Random Hypergraph Compression (ARHC), a domain-independent approach to compressing PDBs using acyclic random r-partite r-uniform hypergraphs. The ARHC algorithm, which comes in Base and Extended versions, provides fast lookup and a high compression rate. ARHC-Extended achieves higher quality heuristics than ARHC-Base by decreasing the heuristic information loss at the cost of some decrease in the compression rate. ARHC shows higher performance than level-by-level Bloom filter PDB compression in all experiments conducted so far.

scholarly journals Threshold and Hitting Time for High-Order Connectedness in Random Hypergraphs

10.37236/5064 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Oliver Cooley ◽  
Mihyun Kang ◽  
Christoph Koch
Keyword(s):  
High Probability ◽  
Hitting Time ◽  
Uniform Hypergraph ◽  
Uniform Hypergraphs ◽  
Time Result ◽  
Edge Probability ◽  
The Moment ◽  
Definition Of ◽  
Random Hypergraph ◽  
Random Hypergraphs

We consider the following definition of connectedness in $k$-uniform hypergraphs: two $j$-sets (sets of $j$ vertices) are $j$-connected if there is a walk of edges between them such that two consecutive edges intersect in at least $j$ vertices. The hypergraph is $j$-connected if all $j$-sets are pairwise $j$-connected. We determine the threshold at which the random $k$-uniform hypergraph with edge probability $p$ becomes $j$-connected with high probability. We also deduce a hitting time result for the random hypergraph process – the hypergraph becomes $j$-connected at exactly the moment when the last isolated $j$-set disappears. This generalises the classical hitting time result of Bollobás and Thomason for graphs.

scholarly journals Compressed Pattern Databases

2007 ◽  
Vol 30 ◽  
pp. 213-247 ◽  
Author(s):  
A. Felner ◽  
R. E. Korf ◽  
R. Meshulam ◽  
R. C. Holte
Keyword(s):  
Search Time ◽  
Combinatorial Problems ◽  
Lookup Table ◽  
Optimal Solutions ◽  
Compression Method ◽  
Heuristic Function ◽  
Towers Of Hanoi ◽  
Intelligent Methods ◽  
Domain Independent ◽  
Pattern Databases

A pattern database (PDB) is a heuristic function implemented as a lookup table that stores the lengths of optimal solutions for subproblem instances. Standard PDBs have a distinct entry in the table for each subproblem instance. In this paper we investigate compressing PDBs by merging several entries into one, thereby allowing the use of PDBs that exceed available memory in their uncompressed form. We introduce a number of methods for determining which entries to merge and discuss their relative merits. These vary from domain-independent approaches that allow any set of entries in the PDB to be merged, to more intelligent methods that take into account the structure of the problem. The choice of the best compression method is based on domain-dependent attributes. We present experimental results on a number of combinatorial problems, including the four-peg Towers of Hanoi problem, the sliding-tile puzzles, and the Top-Spin puzzle. For the Towers of Hanoi, we show that the search time can be reduced by up to three orders of magnitude by using compressed PDBs compared to uncompressed PDBs of the same size. More modest improvements were observed for the other domains.

scholarly journals The Multiple-Orientability Thresholds for Random Hypergraphs

2015 ◽  
Vol 25 (6) ◽  
pp. 870-908 ◽  
Author(s):  
NIKOLAOS FOUNTOULAKIS ◽  
MEGHA KHOSLA ◽  
KONSTANTINOS PANAGIOTOU
Keyword(s):  
Load Balancing ◽  
Hard Disk ◽  
Maximum Load ◽  
Disk Arrays ◽  
Uniform Hypergraph ◽  
Cuckoo Hashing ◽  
Uniform Hypergraphs ◽  
Random Hypergraphs ◽  
Do So ◽  
Parallel Access

Ak-uniform hypergraphH= (V, E) is called ℓ-orientable if there is an assignment of each edgee∈Eto one of its verticesv∈esuch that no vertex is assigned more than ℓ edges. LetHn,m,kbe a hypergraph, drawn uniformly at random from the set of allk-uniform hypergraphs withnvertices andmedges. In this paper we establish the threshold for the ℓ-orientability ofHn,m,kfor allk⩾ 3 and ℓ ⩾ 2, that is, we determine a critical quantityc*k,ℓsuch that with probability 1 −o(1) the graphHn,cn,khas an ℓ-orientation ifc<c*k,ℓ, but fails to do so ifc>c*k,ℓ.Our result has various applications, including sharp load thresholds for cuckoo hashing, load balancing with guaranteed maximum load, and massive parallel access to hard disk arrays.

Hypernetwork models based on random hypergraphs

2019 ◽  
Vol 30 (08) ◽  
pp. 1950052
Author(s):  
Feng Hu ◽  
Jin-Li Guo ◽  
Fa-Xu Li ◽  
Hai-Xing Zhao
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
World Systems ◽  
Uniform Hypergraphs ◽  
Different Types ◽  
Powerful Means ◽  
Simulation Results ◽  
Parameter Values ◽  
Random Hypergraphs

Hypernetworks are ubiquitous in real-world systems. They provide a powerful means of accurately depicting networks of different types of entity and will attract more attention from researchers in the future. Most previous hypernetwork research has been focused on the application and modeling of uniform hypernetworks, which are based on uniform hypergraphs. However, random hypernetworks are generally more common, therefore, it is useful to investigate the evolution mechanisms of random hypernetworks. In this paper, we construct three dynamic evolutional models of hypernetworks, namely the equal-probability random hypernetwork model, the Poisson-probability random hypernetwork model and the certain-probability random hypernetwork model. Furthermore, we analyze the hyperdegree distributions of the three models with mean-field theory, and we simulate each model numerically with different parameter values. The simulation results agree well with the results of our theoretical analysis, and the findings indicate that our models could help understand the structure and evolution mechanisms of real systems.

scholarly journals Orientability Thresholds for Random Hypergraphs

2015 ◽  
Vol 24 (5) ◽  
pp. 774-824 ◽  
Author(s):  
PU GAO ◽  
NICHOLAS WORMALD
Keyword(s):  
Load Balancing ◽  
General Version ◽  
Line Load ◽  
Random Hypergraph ◽  
Random Hypergraphs

Leth>w> 0 be two fixed integers. LetHbe a random hypergraph whose hyperedges are all of cardinalityh. Tow-orienta hyperedge, we assign exactlywof its vertices positive signs with respect to the hyperedge, and the rest negative signs. A (w,k)-orientation ofHconsists of aw-orientation of all hyperedges ofH, such that each vertex receives at mostkpositive signs from its incident hyperedges. Whenkis large enough, we determine the threshold of the existence of a (w,k)-orientation of a random hypergraph. The (w,k)-orientation of hypergraphs is strongly related to a general version of the off-line load balancing problem. The graph case, whenh= 2 andw= 1, was solved recently by Cain, Sanders and Wormald and independently by Fernholz and Ramachandran. This settled a conjecture of Karp and Saks.

Improved Algorithm for Mining Maximum Frequent Patterns Based on FP-Tree

2013 ◽  
Vol 756-759 ◽  
pp. 3692-3695 ◽  
Author(s):  
Nai Li Liu ◽  
Lei Ma
Keyword(s):  
Data Mining ◽  
Fast Algorithm ◽  
Association Rule ◽  
Frequent Patterns ◽  
Memory Space ◽  
The Cost ◽  
Mining Association Rule ◽  
Very High ◽  
Improved Algorithm

Mining association rule is an important matter in data mining, in which mining maximum frequent patterns is a key problem. Many of the previous algorithms mine maximum frequent patterns by producing candidate patterns firstly, then pruning. But the cost of producing candidate patterns is very high, especially when there exists long patterns. In this paper, the structure of a FP-tree is improved, we propose a fast algorithm based on FP-Tree for mining maximum frequent patterns, the algorithm does not produce maximum frequent candidate patterns and is more effectively than other improved algorithms. The new FP-Tree is a one-way tree and only retains pointers to point its father in each node, so at least one third of memory is saved. Experiment results show that the algorithm is efficient and saves memory space.

scholarly journals Saturation Number of Berge Stars in Random Hypergraphs

10.37236/9302 ◽  
2020 ◽  
Vol 27 (4) ◽  
Author(s):  
Lele Liu ◽  
Changxiang He ◽  
Liying Kang
Keyword(s):  
Uniform Hypergraph ◽  
Uniform Hypergraphs ◽  
Minimum Number ◽  
Saturation Number ◽  
Random Hypergraphs

Let $G$ be a graph. We say an $r$-uniform hypergraph $H$ is a Berge-$G$ if there exists a bijection $\phi: E(G)\to E(H)$ such that $e\subseteq\phi(e)$ for each $e\in E(G)$. Given a family of $r$-uniform hypergraphs $\mathcal{F}$ and an $r$-uniform hypergraph $H$, a spanning sub-hypergraph $H'$ of $H$ is $\mathcal{F}$-saturated in $H$ if $H'$ is $\mathcal{F}$-free, but adding any edge in $E(H)\backslash E(H')$ to $H'$ creates a copy of some $F\in\mathcal{F}$. The saturation number of $\mathcal{F}$ is the minimum number of edges in an $\mathcal{F}$-saturated spanning sub-hypergraph of $H$. In this paper, we asymptotically determine the saturation number of Berge stars in random $r$-uniform hypergraphs.

scholarly journals Loose Hamilton Cycles in Random 3-Uniform Hypergraphs

10.37236/477 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Alan Frieze
Keyword(s):  
Absolute Constant ◽  
Hamilton Cycle ◽  
Hamilton Cycles ◽  
Uniform Hypergraphs ◽  
Random Hypergraph

In the random hypergraph $H=H_{n,p;3}$ each possible triple appears independently with probability $p$. A loose Hamilton cycle can be described as a sequence of edges $\{x_i,y_i,x_{i+1}\}$ for $i=1,2,\ldots,n/2$ where $x_1,x_2,\ldots,x_{n/2},y_1,y_2,\ldots,y_{n/2}$ are all distinct. We prove that there exists an absolute constant $K>0$ such that if $p\geq {K\log n\over n^2}$ then $$\lim_{\textstyle{n\to \infty\atop 4|n}}\Pr(H_{n,p;3}\ contains\ a\ loose\ Hamilton\ cycle)=1.$$

scholarly journals Practical Time Optimization of DSP Program for High-frequency Applications

2021 ◽  
Vol 2095 (1) ◽  
pp. 012005
Author(s):  
Zhuyu Xun ◽  
Hongfa Ding ◽  
Zhou He
Keyword(s):  
Execution Time ◽  
High Frequency ◽  
Rapid Development ◽  
Power Conversion ◽  
High Frequency Power ◽  
Memory Space ◽  
Time Optimization ◽  
The Cost ◽  
Frequency Power

Abstract The rapid development of the high frequency power conversion techniques makes great demands on the methods that can reduce the execution time of the program effectively. This paper is aiming at reducing the execution time of the program in several aspects such as sampling, complex expressions, and so on. As one of the most widely applied methods, reducing the execution time of the program at the cost of the memory space is adopted in this paper. Furthermore, in order to confirm the feasibility and superiority of programs that are proposed in this paper, they are compared with other programs that can realize the same function in terms of the execution time.

scholarly journals Reducing the Cost of Implementing Filters in LoRa Devices

Sensors ◽  
2019 ◽  
Vol 19 (18) ◽  
pp. 4037
Author(s):  
Shania Stewart ◽  
Ha H. Nguyen ◽  
Robert Barton ◽  
Jerome Henry
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
System Performance ◽  
Pulse Shaping ◽  
Error Rates ◽  
Lookup Table ◽  
Significant Performance ◽  
High Level ◽  
The Cost ◽  
The Impact

This paper presents two methods to optimize LoRa (Low-Power Long-Range) devices so that implementing multiplier-less pulse shaping filters is more economical. Basic chirp waveforms can be generated more efficiently using the method of chirp segmentation so that only a quarter of the samples needs to be stored in the ROM. Quantization can also be applied to the basic chirp samples in order to reduce the number of unique input values to the filter, which in turn reduces the size of the lookup table for multiplier-less filter implementation. Various tests were performed on a simulated LoRa system in order to evaluate the impact of the quantization error on the system performance. By examining the occupied bandwidth, fast Fourier transform used for symbol demodulation, and bit-error rates, it is shown that even performing a high level of quantization does not cause significant performance degradation. Therefore, the memory requirements of LoRa devices can be significantly reduced by using the methods of chirp segmentation and quantization so as to improve the feasibility of implementing multiplier-less filters in LoRa devices.

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