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By VINCENT M. MALLOZZI

Once upon an algorithm, a widower in San Francisco who was an expert in online consumer behavior took to the internet to find the one.

“I was still hurting,” said Bill Tancer, whose wife of 17 years had succumbed to complications of breast cancer in July 2014. “But I felt it was time to put myself out there and start dating again.”

Mr. Tancer did exactly that in January 2015, when he created a dating profile and sent it to eHarmony. He fully expected to receive numerous matches, wishing to find among them a woman who could potentially become, as he put it, “my one and only.”

But Mr. Tancer, then 48, received a reply that seemed to come not from an algorithm in a search engine, but from a genie in a bottle. He was granted exactly what he had wished for: one match, and one match only, an improbable result that brought to his screen the profile of Erika Holiday, a 38-year-old forensic psychologist and adjunct professor of psychology at the University of Southern California, some 300 miles away.

“I didn’t know if there was something wrong with my computer,” he joked, “or if there was something wrong with me.”

Nevertheless, that Dr. Holiday had emerged as Mr. Tancer’s only match based solely on his criteria for finding a suitable mate, suggested that he had perhaps found a perfect mate.

“She was single and successful, brilliant and gorgeous, and she had never been married,” he said. “Being an algorithm believer, I thought I should just trust it, and that maybe she was truly, and literally, the one for me.”

Though Mr. Tancer began receiving additional matches after changing some of his relationship criteria, he chose to reach out only to Dr. Holiday, “but not before doing a ton of research on her,” he said.

He was soon reading online excerpts from a book Dr. Holiday had co-written in 2009 called “Mean Girls, Meaner Women” He also watched numerous YouTube videos of Dr. Holiday, as a psychology expert, chatting on-air with “Dr. Phil,” and various other television hosts on CNN, Fox News and the E! channel.

Dr. Holiday, who said she had received “well over a hundred matches,” on eHarmony, took an immediate and less cautious approach to Mr. Tancer. They were, in her estimation, a match made in cyber heaven.

“I’m a very intuitive person, and the moment I saw him, without ever having met him, I said to myself, ‘He’s the one, he’s the one,’” Dr. Holiday said. “I thought he was so handsome and he seemed so intelligent.”

She enlisted the help of her mother, Eva Yomtobian, “to help me look up some stuff about him,” she said. “But deep down inside, I just had that feeling.”

Though her mother was equally ecstatic, she chose to remain cautiously optimistic.

“It sounded so good, everything just fit and I was really excited for Erika,” said Ms. Yomtobian, a retired social worker for the Los Angeles County Department of Children and Family Services.

“Bill was really nice,” she said. “He was educated. He was intelligent. He was Jewish. But I wasn’t going to get overly excited just yet.”

Dr. Holiday and Mr. Tancer exchanged several messages, shared a handful of late-night phone calls and eventually made arrangements to meet a few weeks later at a tiny coffee shop in the Sherman Oaks area of Los Angeles, where Dr. Holiday had lived her entire life.

“Driving past the shop, I saw her standing outside,” Mr. Tancer said. “I wasn’t prepared for the fact that she was even more beautiful than her profile pictures. I parked and nervously walked up to her and introduced myself.”

Before long, Mr. Tancer was feeling comfortable and opening up about the sorrow and pains of being a widower, which struck an emotional chord with Dr. Holiday.

“He had been married for a long time,” she said. “It was only about six months since his wife had passed away, and listening to him talk about how much he cared for her, and how he never left her side and was a faithful husband, well, I thought what an amazing man. Through that story I could see how loving and kind he was, it told me a lot about his character and what kind of person he truly was. I was hooked.”

True to the algorithm that brought them together, they became an immediate item.

“I was used to being the quintessential caretaker for guys I dated,” Dr. Holiday said. “And along comes this guy who is treating me with such respect and kindness. It was overwhelming but in a good way. He was Prince Charming, and I wasn’t used to Prince Charming.”

They were soon bonding over their “fascination of people and what makes them tick,” as Mr. Tancer put it, and talking most things California.

He learned that she graduated from California State University, Northridge, and received a master’s degree in psychology from Pepperdine University, as well as a doctor of psychology degree from Phillips Graduate Institute in Los Angeles. (He also learned the she was born Erika Yomtobian, but had legally changed her surname, which means holiday in Hebrew.)

She learned that he grew up in Palm City, Fla., a son of Sheila and Martin Tancer, real estate agents who moved the family to Atlantis, Fla., when he was 12. He graduated from the University of Florida, and received a law degree from Mercer University in Georgia before joining the Navy in 1990. He was first stationed at the Kings Bay Trident Submarine Base in Georgia, where he was a lieutenant in the United States Naval Reserve and a special assistant United States attorney for the Southern District of Georgia.

The Navy eventually steered him to California, as he was transferred to the Naval Medical Center in Oakland in 1993 for his last year and a half of service.

He was living in Burlingame, Calif., in 2008 when he wrote the first of two books centered on data and algorithms: “Click: What Millions of People Are Doing Online and Why it Matters,” which became a New York Times best seller. He had moved to San Mateo, Calif., by 2014, the year he wrote “Everyone’s a Critic: Winning Customers in a Review-Driven World.”

“With Erika being a psychologist and me studying consumer behavior, we just had so much in common,” Mr. Tancer said. “We practically spoke the same language.”

During the next four months, each took turns hopping aboard commuter flights to spend weekends together, much to the delight of their friends and family.

“Bill would fly for like half an hour, have dinner with Erika, and then fly back to San Francisco,” said Vikain Hanounik, Dr. Holiday’s best friend. “And the next day Erika would fly out just to have lunch with him, they would just go back and forth. I’ve never seen her happier.”

The same was true for Mr. Tancer, said Ed Tancer, his older brother.

“I could tell by the way Billy talked about Erika that she was someone special,” he said. “Billy’s wife was sick for the majority of their marriage, it was a very rough time for him, so we were thrilled when he found Erika.”

In April 2015, Dr. Holiday invited Mr. Tancer to her parents’ home in Malibu, Calif., to meet them for the first time while celebrating Passover. Before dinner ended, her mother and father, Luigi Bian (a filmmaker), were convinced that their daughter had found the perfect match.

“They were so cute, holding hands the whole time, it was really sweet,” Ms. Yomtobian said. “He looked like he was really into her. As an older woman, I knew it. It was there.”

In July 2015, Mr. Tancer decided to move to Los Angeles to be with Dr. Holiday and has since been working there as an independent marketing consultant to the technology, financial services, travel and hospitality industries.

“I sold my house and moved there, and I haven’t looked back since,” Mr. Tancer said. “In 2014, I didn’t think it was possible to ever be happy again but Erika proved me wrong.

“She’s brought me unconditional love and she makes me laugh,” he said. “But most importantly, she’s given me the gift of unbounded happiness and a reason to love life again.”

They were married Nov. 5 at the Beverly Hills home of the bride’s brother, Daniel Yomtobian, who described his sister in the years before Mr. Tancer came clicking as “very focused on her work and her career, and pretty happy doing her own thing.”

“I’m sure she had been dating, but I hadn’t heard about anybody in 10 years before she met Bill,” he said.

Most of the couple’s 140 guests gathered in the backyard of the Mediterranean-style house, a 15,000-square-foot mansion with palatial floor-to-ceiling windows in the living room and a flowing terrace that offered breathtaking views stretching from Los Angeles to the Santa Monica skyline, with the Pacific Ocean barely visible in the hazy distance.

“By coming underneath this huppah, you two have built your first home together,” Rabbi Joshua Knobel told the couple, who began exchanging vows as the sun set on a warm evening.

“When I look at you, I see everything that is right with the universe,” the groom told his new bride. “I see beauty, kindness, intelligence, but most of all, I see magic.”

His perfect match had the perfect response.

“I feel like my life didn’t truly start until meeting you,” the bride said. “I honestly didn’t think it would be possible to experience a love and a relationship like this.”

“This is the best love story I have ever known,” she added, “and I can’t believe it’s mine.”