????Leo Apotheker is barnstorming the world as he embarks on fixing the culture and focus of the huge technology company. One to-do stands out above all the rest.

????Here's what new Hewlett-Packard CEO Leo Apotheker's to-do list might look like:

????1. Move to Palo Alto

????2. Increase investment in research and development

????3. Build a "strong and viable" software business

????The first two tasks should be easy enough to cross off the list. Finding real estate in the Silicon Valley can't be hard for a tech mogul with a $4.6 million relocation allowance, and HP (HPQ) certainly has the cash to pour into R&D. But building a successful software business will be tough for a company whose core business is selling PCs, printers and servers.

????Currently, software accounts for roughly 3% of HP's $126 billion in annual revenues. Developing (and acquiring) better software will take a lot of time—and money. In other words, Apotheker has his work cut out for him.

????"HP's been running the way it's been running for a long, long time," says Martin Reynolds, an analyst with Gartner Research.

????According to Reynolds, Apotheker will need to shift HP from engineering-centric mode into more of a sales and marketing-focused organization in order to become a strong software player. He'll also need to hire a head of software that reports directly to the CEO's office. That job could go to Bill Veghte, a former Microsoft exec who currently runs HP's software business and reports to Ann Livermore, executive VP of the company's enterprise business division.

????But even if Apotheker does all of the above, it's unlikely that growing its software business from within will do enough to boost HP's foothold in the market. Acquisitions won't necessarily come easy either—competitors Oracle (ORCL) and IBM (IBM) have been busy snapping up attractive enterprise software players like Art Technology Group and Netezza, so HP will need to move fast to make strategic software buys.

????HP has made several large-scale software acquisitions in recent years, including Mercury Interactive and Opsware. But the company remains weak in fast-growing areas like business intelligence and cloud-based software.

????Apotheker publicly acknowledges the challenge.

????"We need to enhance our software IP across the company, to create more differentiation with our products," Apotheker told investors and reporters during an HP earnings conference call on Monday. "This includes strengthening our core software business segment, as well as adding value-added IP and services that cut across all segments."

????Apotheker is off to a good start. HP's fourth-quarter earnings beat analysts' estimates (net income for the quarter rose to $2.5 billion, up 5% from a year earlier). The Oracle-SAP case has wrapped up (Oracle had called on Apotheker to testify, but the case closed Tuesday when a federal jury decided SAP must pay $1.3 billion to Oracle), which means Oracle CEO Larry Ellison might cut back on his public jabs at Apotheker and HP. And salary raises will soon be reinstituted at HP, which could help turn at least some employees into Apotheker fans.