Las Vegas algorithm for finding 00000 in bit string

Problem 1: Consider the following problem: given a binary string $w=a_1a_2cdots a_n in{0,1}^*$, decide whether $w$ contains 00000 as a substring (i.e., where $w$ contains five consecutive 0’s). There is an obvious $O(n)$-time algorithm. You will investigate the hidden constant factor, concerning the number of bits that need to be examined (i.e., the number of $a_i$‘s that need to be evaluated) to solve this problem.

  1. (10/100 points) First argue that every deterministic algorithm solving this problem needs to evaluate $Omega(n)$ bits in the worst case.
  2. (30/100 points) Prove that for a sufficiently large constant $c$, for any string $a_1 cdots a_c$ of length $c$ that does not contain 00000, there must exist two indices $i,j in {1,ldots,c}$ with $a_i=a_j=1$ and $2 leq |i-j| leq 5$.
  3. (60/100 points) Design a Las Vegas randomized algorithm solving this problem (with zero error probability) that evaluates an expected $alpha n + o(n)$ number of bits for any input, for some constant $alpha$ strictly smaller than $1$. (You do not need to optimize the constant $alpha$.)

Above is a question some friends and I have looked at to prepare for a qualifying exam and is itself from a past qualifying exam. Parts 1 and 2 are fine but what we are having troubles with is part 3. I think the idea behind this problem is to imagine that evaluating some bit $s_i$ is really expensive, so we would like to get the right answer while minimizing how many of these bits we evaluate. That said, there is some ambiguity to us about whether we (1) care about the number of distinct bits we evaluate or (2) the total number of times we evaluate any bit. Clearly if we were worried about the latter, we could just store the result of the bit evaluation and avoid doing an expensive evaluation again, but we are not sure. For now, I assume the latter case and specifically that if we want the value for the same bit twice, we assume we need to evaluate it each time and incur $2$ units to the cost we are trying to minimize.


Now I have some idea for this problem and to help explain my idea, let us consider a simple deterministic algorithm with the pseudocode written below. We will loop from the start of the string to the end, checking all meaningful 5 bit substrings. If we ever find a $1$ bit as we loop over a 5 bit substring, we know that substring cannot be $00000$ but if we start at the bit right after that $1$ bit, there might be one. Thus, we update our new starting point to the position right after that $1$ bit and then start back up again from there.

On input $s$:

  1. set $i leftarrow 1$
  2. while($i leq (n-4)$):
    • set $b leftarrow text{true}$
    • for($j = 0$ to $4$):
      • if( $a_{i+j} = 1$ ):
        • $i leftarrow (i+j+1)$
        • $b leftarrow text{false}$
        • break for loop.
    • if( $b = text{true}$ ):
  3. return FALSE

My idea for a Las Vegas algorithm was to do the same algorithm but slightly modify it by making the inner loop performed in random order, making the pseudocode now be

On input $s$:

  1. set $i leftarrow 1$
  2. while($i leq (n-4)$):
    • set $b leftarrow text{true}$
    • for($j = 0$ to $4$ in random order):
      • if( $a_{i+j} = 1$ ):
        • $i leftarrow (i+j+1)$
        • $b leftarrow text{false}$
        • break for loop.
    • if( $b = text{true}$ ):
  3. return FALSE

The positive thing going for this algorithm is that if there exists a $1$ bit in the 5 bit substring we are looking at in the inner loop, we will find it in at most $3$ loop iterations in expectation. However, if I define a bit string $s$ to be
$$s = 100001 100001 100001 cdots 100001$$
then the algorithm should require looking at $6$ bits (potentially some of the same ones multiple times) in expectation to get past each $100001$ substring. This implies on this input we will go to see the value of $n$ bits (the number of distinct bits seen may be less) in expectation before we answer the question of if $00000$ is contained in $s$. Thus, this algorithm does not seem sufficient.

Does anyone have any thoughts on how to approach this problem or think we should actually be worried about the number of distinct bits we evaluate? If yes to the latter, then I could potentially see other ways to tackle this problem.

air travel – Can I use my TWIC card as my photo ID to fly from Philadelphia to Las Vegas?

I live in the United States and I’m traveling from Philadelphia International Airport to McCarran Airport in Las Vegas. My passport has expired and I have misplaced my driver’s license. I am trying to save money and time by using my Transportation Worker Identification Credentials (TWIC Card) as my photo ID to board the plane.

It was issued to work at the power plant, which is located in the port. Anybody working at any port in the US needs this card to be able to enter it. Applying for it is similar to applying for a passport. So it is not an easy credential to obtain. There is a little chip in it that is like a SIM card and has everything the government would want to know about me on it. It is a federally-issued card and has my photo on it.

Will I be able to use this to board the plane, or will I have to deal with the long lines at the DMV and get a new license made?

Las Vegas Marijuana Cannabis Businesses and Digital Services

Las Vegas marijuana cannabis businesses are rooting their ground and many new popping up all over the Las Vegas valley getting ready for the new law to take effect making secured digital services like business voice, secured encrypted emails, and even hosted IP cam monitoring systems in high demand.

Clark County set a high and very strict set of rules for marijuana dispensaries, the newest legal vice in this capital of vice, will also be kept separate, even when the state gets its system of recreational dispensaries set up. The zoning rules for Clark County don’t allow dispensaries anywhere near a casino. Clark County has at least a dozen dispensaries parallel to the Strip, but they’re at least several blocks away and nowhere in sight. In addition, the Nevada Gaming Control Board does not allow investors in the casino industry to invest in dispensaries, and vice versa this includes all lines of communication must be encrypted to protect business-sensitive data.

These types of businesses need a higher grade level of hosting, putting companies like NocRoom Voice & Data to work with offering medical-grade Hosted PBX w/VoIP Phone System and encrypted emails with full turn-key solutions for its clients including off-premises hosting for the surveillance system and file sharing between locations of client businesses.
SEMrush

How does NocRoom do this?

NocRoom uses the latest technology offering for IP-based networks helping our customers like for example the medical billing company BillNet Solutions to process more than 5000+ calls, 7000 emails, and file-sharing 1TB of data per day between its two locations. This customer relies on the latest technology for security and to keep all their locations acting as one single office – with over 100 employees this can be a challenge. All data from hosted PBX, emails, and file sharing are encrypted in and out of the office network. With the new IP-based networks like hosted PBX, emails, and open-source software – all working smoothly together.

Who is NocRoom?

Founded in 2006, NocROOM is located at one of the largest internet exchange points in the world, facilitating excellent inter-connectivity with Latin America, the Caribbean, and Europe. NocRoom is a global provider of optimized network solutions that offer the best possible performance, reliability, and availability. Our advanced, IP-based networks deliver data, voice, and content to clients and partners worldwide. Offerings include colocation, transit, transport, VoIP, and network-based services.

Email:

LinkedIn: https://www.linkedin.com/in/vincentgonzalezipv4

 

usa – What to wear to a casino in Las Vegas?

For the general area, there’s no dress code – you even see people wandering through in their swimming gear after they’ve been in the pool! I’ve been in wearing t-shirt and jeans, feeling under-dressed until I saw the tourists in their t-shirt and shorts with flip-flops.

However, you may wish to consider what else you want to do in Vegas, and dress accordingly. Many nightclubs have dress codes, as do some of the restaurants. Night clubs in fact often suggest business casual – leather shoes, collared shirts, and so on.

If you’re seeing a show, people tend to dress up for those – smart long-sleeved shirt and trousers, although again it’s not a strict rule.

And if you’re just wandering the streets looking, it’s handy to have light clothes in summer – it can get seriously hot!

Naming of Monte Carlo and Las Vegas Complexity classes

For Curiosity Sake, I was wondering if there was some history behind the naming of “Las Vegas” and “Monte Carlo” classes.

I’ve searched on the internet for quite some time now but I did not find a proper answer, is it just because they are probabilistic which gives them the “gambling” nature, or is there something more to the nomenclature?

ServerPoint: 18 Years of Service (E3 Dedi from $59/mo in Las Vegas, NV, USA)

You’d think that over 12 years, LowEndBox would have featured nearly every hosting provider in the known universe, but we’re still getting fresh offers from hosts who are appearing here for the first time.  Case in point: ServerPoint!

They’ve been in business for 18 years.  To put that in perspective, back in 2002 “How You Remind Me” by Nickelback was the #1 song, the first iPhone was still on the drawing board, and your PC probably came with a 60GB hard drive.  That’s some impressive staying power in a turbulent industry.

Besides longevity, they have 100% in-house support and are privately owned.  Their web site is pleasingly full, with a blog, system status, and a pretty generous affiliate program.

They offer more than just dedicated servers, with VPS and shared products as well, but today they’re bringing us some Xeon E3-1270 v2s in Las Vegas.  Looks like a pretty solid offer from a pretty solid shop, but as always, the community is final judge. So if you decide to try them out, be sure to leave a comment.

They are registered in Nevada as A+ Hosting (C8539-2002).  They accept credit cards and Paypal, and you can find their terms of service on their web site.

Here’s what they had to say, in their own words: 

“ServerPoint has been serving tens of thousands of clients with reliable, fast web hosting, dedicated servers and cloud server services for nearly 18 years. We provide 24×7 support round the clock. Our team is highly experienced and most have been with us for many years, allowing for a quick resolution to any challenges that may arise. We are obsessed with quality, redundancy and speed. We cut no corners in how we build our infrastructure. We’ll spend whatever is necessary to make our platform as stable as technology allows

Info on network after the jump but first, here are the offers:

Dedicated
Las Vegas, NV, USA

Dedicated
Las Vegas, NV, USA

Network information and node details available by reading more.

NETWORK INFO

Flexential, Las Vegas, Nevada

Test IPv4: 216.108.237.244

Please let us know if you have any questions/comments and enjoy!

raindog308

I’m Andrew, techno polymath and long-time LowEndTalk community Moderator. My technical interests include all things Unix, perl, python, shell scripting, and relational database systems. I enjoy writing technical articles here on LowEndBox to help people get more out of their VPSes.

FREE Las Vegas, NV Business Directory

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Here is a FREE Business Directories you can submit your local business to

1. LasVegasDIR.com

Pubcon Pro Las Vegas 2020 Goes Online

Brett Tabke has announced that Pubcon Pro for Las Vegas 2020 is to move online.

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