So I'm looking for potential solutions to a complex pathing/route-finding problem.
Say I have a number of required appointments. These appointments happen generally on a weekly cycle, but can diverge from this (IE two weekly). Each appointment has a certain amount of time that must be spent there.
Each of these appointments has a number of criteria attached that must be upheld:
Time dependence - Appointments must be set either between a range of times, or at a particular, critical time
Skills dependence - Certain appointments can only be attended by certain staff members (IE qualification requirements)
Preferences - It is preferred as an example that appointments are attended to by those with more previous appointments with the same client - these are not "hard" limitations and can by bypassed if needed
Given the above problems I'm looking to develop a solution that minimises the travel cost between the appointments (IE Multi-Salesman) whilst ensuring the above criteria are met on a daily basis.
My initial reaction was to break this down into different problems. The first being the Time the appointments are happening, and the second being the route-finding between those appointments. Given the complex nature of the requirements I worry that this will end up with certain appointments being unreachable (IE the only staff member who can complete the call is too far away).
Are there any existing algorithms / solutions that can deal with complex route-planning of this nature?
This could be approached from a constraint programming angle
In computer science, constraint programming is a programming paradigm
wherein relations between variables are stated in the form of
constraints. Constraints differ from the common primitives of
imperative programming languages in that they do not specify a step or
sequence of steps to execute, but rather the properties of a solution
to be found.
There are many libraries for different languages available (listed in that wikipedia article)
What you describe is a Constraint satisfaction problem
Related
Preface
I'm new to Gremlin and working through Kelvin Lawrence's awesome eBook on the topic in order to solve a specific use-case.
Due to the sheer amount to learn, I'm asking this question to get recommendations on how I might approach the challenge so that, as I read the eBook, I'll better know the sections to which to pay extra attention.
I intend to use AWS Neptune in the pursuit of solving this, so I tagged that topic as well.
Question
Respecting departure/arrival times of legs + other constraints, can the shortest path (the real-world, logistical meaning
of "path") between origin and destination be "queried" (i.e., can I
use the Gremlin console with a single statement)? Or is the
use-case of such complexity that I will effectively need to write a
program to accomplish it?
Use-Case / Detail
I hope to answer the question:
Starting at ORIGIN on DAY, can I get to DESTINATION while
respecting [CONDITIONS]?
The good news is that I only need a true/false response (so limit(1)?) and a lack of a result (e.g., []) suffices for "no".
What are the conditions?
Flight schedules need to be respected. Instead of simple flight routes (i.e., a connection exists between BOSton and DALlas), I have actual flight schedules (i.e., on Wednesday, 9 Nov 2022 at 08:40, flight XYZ will depart BOSton and then arrive DALlas at 13:15) ... consequently, if/when there are connections, I need to respect arrival and departure times + some sort of buffer (i.e., a path for which a Traveler would arrive at 13:05 and depart on another leg at 13:06 isn't actually a valid path);
Aggregate travel time / cost limits. The answer to the question needs to be "No" if a path's aggregate travel time or aggregate cost exceeds specified limits. (Here, I believe I'll need to use sack() to track the cost - financial and time - of each leg and bail out of the repeat() until loop when either is hit?)
I apologize b/c I know this isn't a good StackOverflow question, since it's not technically specific -- my hope is that, at least, some specific technical recommendations might result.
The use-case seems like the varsity / pro version of the flight routes example presented in the eBook, which is perfect for someone brand-new to Gremlin ... 😅
There are a number of ways you might model this. One way I have seen used effectively is to essentially have two graphs. This first just knows about routes. You use that one to find ways to get from A to Z in x-hops. Then using the second graph, which tracks actual flights, using the results from the first search you look for flights within the time constraints you need to impose. So there is really the data modeling question and then the query writing part. Obviously the data model should enable the queries to be as efficient as possible.
There are a couple of useful blog posts related to your question. They mention Neo4j but are really quite generic and mainly focus on the data modeling aspects of your question.
https://maxdemarzi.com/2015/08/26/modeling-airline-flights-in-neo4j/
https://maxdemarzi.com/2017/05/24/flight-search-with-neo4j/
I would focus on the data model, and once you have that, focus on the Gremlin queries. Amazon Neptune also now supports openCypher as an alternative property graph query language.
If you already have a data model worked out and can share a sample, I'm happy to update the answer with an example query or two.
I know how Hyperloglog works but I want to understand in which real-world situations it really applies i.e. makes sense to use Hyperloglog and why? If you've used it in solving any real-world problems, please share. What I am looking for is, given the Hyperloglog's standard error, in which real-world applications is it really used today and why does it work?
("Applications for cardinality estimation", too broad? I would like to add this simply as a comment but it won't fit).
I would suggest you turn to the numerous academic research of the subject; usually academic papers contain some information of "prior research on the subject" as well as "applications for which the subject has been used". You could start with traversing the references of interest as referenced by the following article:
HyperLogLog: the analysis of a near-optimal cardinality estimation algorithm, by P. Flageolet et al.
... This problem has received a great deal of attention over the past
two decades, finding an ever growing number of applications in
networking and traffic monitoring, such as the detection of worm
propagation, of network attacks (e.g., by Denial of Service), and of
link-based spam on the web [3]. For instance, a data stream over a
network consists of a sequence of packets, each packet having a
header, which contains a pair (source–destination) of addresses,
followed by a body of specific data; the number of distinct header
pairs (the cardinality of the multiset) in various time slices is an
important indication for detecting attacks and monitoring traffic, as
it records the number of distinct active flows. Indeed, worms and
viruses typically propagate by opening a large number of different
connections, and though they may well pass unnoticed amongst a huge
traffic, their activity becomes exposed once cardinalities are
measured (see the lucid exposition by Estan and Varghese in [11]).
Other applications of cardinality estimators include data mining of
massive data sets of sorts—natural language texts [4, 5], biological
data [17, 18], very large structured databases, or the internet graph,
where the authors of [22] report computational gains by a factor of
500+ attained by probabilistic cardinality estimators.
At my work, HyperLogLog is used to estimate the number of unique users or unique devices hitting different code paths in online services. For example, how many users are affected by each type of service error? How many users use each feature? There are MANY interesting questions HyperLogLog allows us to answer.
Stackoverflow might use hyperloglog to count the views of each question. Stackoverflow wants to make sure that one user can only contribute one view per item so every view is unique.
It could be implemented with set. every question would have a set that stores the usernames:
question#ID121e={username1,username2...}
For each question creating a set would take up some space and consider how many questions have been asked on this platform. The total amount of space to keep track of every view per user would be huge. But hyperloglog uses about 12 kB of memory per key no matter how many usernames are added, even 10 million views.
I am building a local OLAP cube based on data gathered from several OLTP sources. Please note that I am doing this programmatically and do not have access to tools like SSAS or MDX-based tools.
My requirements are somewhat different than the operational requirements of the OLTP system users. I know that "in theory" it would be preferable to retain the most atomic grain available to me, but I don't see a reason to include the lowest level of data in the cube.
For example (I am simplifying), I have a measure field like "Price". Additionally, each sales fact has a Version attribute with values such as:
List (Original/Initial)
Initial Quote
Adjusted Quote
Sold
These describe the internal development of our pricing and are critical to the reports that I create.
However, for my reporting purposes, I will always want to know the value of all Versions whenever I am referencing a given transaction. Therefore, I am considering pivoting measures like Price by Version in the cube (Version will still be its own entity in the data model), resulting in measures like:
PriceList
PriceQuotedInitial
PriceQuotedAdjusted
PriceSold
Since only one Version is ever effective at a given point in time, we do not need to aggregate across multiple Versions.
Known Advantages
Since this will be a local cube file, it appears this approach would
simplify the creation of several required calculated measures that compare Price
across different Versions (would not be an issue to create calculated measures at various levels of aggregation if I was doing this with MDX)
It would also reduce the number of records by a factor of between 3
and 6, which would significantly boost performance for a local cube.
Known Disadvantages
While the data model will match the business process, the cube would not store the data at the most atomic level. An analyst would need to distinguish between Versions by Measure selection, and could not filter by Version - they would always get all available Versions.
This approach will greatly increase the number of Measures. For
example, there is not just one Price we are tracking, but several
price components and other Measures we track for each transaction.
So if we track a dozen true Measures for each transaction, that
might end up being 50-60 Measures if I take this approach.
I understand that for very large Fact tables, it would be preferable to factor all possible fields out of the Fact table into Dimensions for performance purposes, but I am not sure whether this is the case when using a local cube, as in all likelihood, I will put fewer than 50,000 records into any given cube file, given the limitations of local cubes.
Are there other drawbacks to this approach that I'm missing?
I'm beginning the process of instrumenting a web application, and using StatsD to gather as many relevant metrics as possible. For instance, here are a few examples of the high-level metric names I'm currently using:
http.responseTime
http.status.4xx
http.status.5xx
view.renderTime
oauth.begin.facebook
oauth.complete.facebook
oauth.time.facebook
users.active
...and there are many, many more. What I'm grappling with right now is establishing a consistent hierarchy and set of naming conventions for the various metrics, so that the current ones make sense and that there are logical buckets within which to add future metrics.
My question is two fold:
What relevant metrics are you gathering that you have found indespensible?
What naming structure are you using to categorize metrics?
This is a question that has no definitive answer but here's how we do it at Datadog (we are a hosted monitoring service so we tend to obsess over these things).
1. Which metrics are indispensable? It depends on the beholder. But at a high-level, for each team, any metric that is as close to their goals as possible (which may not be the easiest to gather).
System metrics (e.g. system load, memory etc.) are trivial to gather but seldom actionable because they are too hard to reliably connect them to a probable cause.
On the other hand number of completed product tours matter to anyone tasked with making sure new users are happy from the first minute they use the product. StatsD makes this kind of stuff trivially easy to collect.
We have also found that the core set of key metrics for any teamchanges as the product evolves so there is a continuous editorial process.
Which in turn means that anyone in the company needs to be able to pick and choose which metrics matter to them. No permissions asked, no friction to get to the data.
2. Naming structure The highest level of hierarchy is the product line or the process. Our web frontend is internally called dogweb so all the metrics from that component are prefixed with dogweb.. The next level of hierarchy is the sub-component, e.g. dogweb.db., dogweb.http., etc.
The last level of hierarchy is the thing being measured (e.g. renderTime or responseTime).
The unresolved issue in graphite is the encoding of metric metadata in the metric name (and selection using *, e.g. dogweb.http.browser.*.renderTime) It's clever but can get in the way.
We ended up implementing explicit metadata in our data model, but this is not in statsd/graphite so I will leave the details out. If you want to know more, contact me directly.
I have both problems and solutions to over twenty years of physics PhD qualifying exams that I would like to make more accessible, searchable, and useful.
The problems on the Quals are organized into several different categories. The first category is Undergraduate or Graduate problems. (The first day of the exam is Undergraduate, the second day is Graduate). Within those categories there are several subjects that are tested: Mechanics, Electricity & Magnetism, Statistical Mechanics, Quantum Mechanics, Mathematical Methods, and Miscellaneous. Other identifying features: Year, Season, and Problem number.
I'm specifically interested in designing a web-based database system that can store the problem and solution and all the identifying pieces of information in some way so that the following types of actions could be done.
Search and return all Electricity & Magnetism problems.
Search and return all graduate Statistical Mechanics problems.
Create a random qualifying exam — meaning a new 20 question test randomly picking 2 Undergrad mechanics problems, 2 Undergrade E&M problems, etc. from past qualifying exams (over some restricted date range).
Have the option to hide or display the solutions on results.
Any suggestions or comments on how best to do this project would be greatly appreciated!
I've written up some more details here if you're interested.
For your situation, it seems that it is more important part to implement the interface than the data storage. To store the data, you can use a database table or tags. Each record in the database (or tag) should have the following properties:
Year
Season
Undergradure or Graduate
Subject: CM, EM, QM, SM, Mathematical Methods, and Miscellaneous
Problem number (is it neccesary?)
Question
Answer
Search and return all Electricity & Magnetism problems.
Directly query the database and you will get an array, then display some or all questions.
Create a random qualifying exam — meaning a new 20 question test randomly picking 2 Undergrad mechanics problems, 2 Undergrade E&M problems, etc. from past qualifying exams (over some restricted date range).
To generate a random exam, you should first outline the number of questions for each category and the years it drawn from. For example, if you want 2 UG EM question. Query the database for all UG EM questions and then perform a random shuffling on the question array. Finally, select the first two of them and display this question to student. Continue with the other categories and you will get a complete random exam paper.
Have the option to hide or display the solutions on results.
It is your job to determine whether you want the students to see answer. It should be controlled by only one variable.
Are "Electricity & Magnetism" and "Statistical Mechanics" mutually exclusive categoriztions, along the same dimension? Are there multiple dimensions in categories you want to search for?
If the answer is yes to both, then I would suggest you look into multidimensional data modeling. As a physicist, you've got a leg up on most people when it comes to evaluating the number of dimensions to the problem. Analyzing reality in a multidimensional way is one of the things physicists do.
Sometimes obtaining and learning an MDDB tool is overkill. Once you've looked into multidimensional modeling, you may decide you like the modeling concept, but you still want to implement using relational databases that use the SQL interface.
In that case, the next thing to look into is star schema design. Star schema is quite different from normalization as a design principle, and it doesn't offer the same advantages and limitations. But it's worth knowing in the case where the problem is really a multidimensional one.