How does the United States assert its interests in the vortex of world power that has developed around the Persian Gulf? One way is to build up American positions of strength in the neighborhood.

But such a buildup is slow, costly and subject to weighty political constraints abroad and here at home. A cheaper and speedier strategy, now beginning to attract attention in the administration, emphasizes spoiling operations against the vunerable extension of Soviet influence in the area -- notably Afghanistan, Libya, South Yemen and Ethiopia.

The security problem of the Persian Gulf reared its ugly head when the Russians invaded Afhganistan in December 1979. The Carter Doctrine of January 1980 proclaimed that the United States regarded the security of the Persian Gulf as a "vital national interest."

The Navy was assigned to full-time duty in the Indian Ocean. Accords for base facilities were concluded in Somalia, Oman and Kenya. A start was made on raising a Rapid Deployment Force, comprising at least four American divisions capable of intervening in the Persian Gulf within a fortnight. Various schemes were advanced to beef up the forces of supposedly strong anti-Soviet leaders in such countries as Pakistan, Turkey and Egypt.

The Reagan administration has added some ideas of its own about the Persian Gulf problem. It has proposed the establishment of a force, including Americans, that would guarantee the Camp David Accords between Israel and Egypt, and would also be available to meet emergencies in the Gulf. It has been willing to extend increased military aid, and to ease up on public charges about nuclear proliferation. Hence the latest offer to Pakistan for military cooperation.

But difficulties have marked every step of the way. Service rivalries have plagued the organization of the RDF. Thoughtful senators -- for example, William Cohen, the Maine Republican -- have questioned the utility of the RDF in the event of subversion in the Gulf countries.

Japan and the European allies have disputed the emphasis on military measures in the area. The State Department Arabists have regularly sabotaged any idea of building on the strength of Israel and, by extension, its Egyptian partner in the Camp David Accords. Events -- like the cave-in of Gen. Zia Ul-haq after the hijacking of a Pakistani airliner -- have exposed the weakness of some local leaders. Most Islamic countries -- including Saudi Arabia -- seemed drawn to a neutralist stance, aimed at keeping both the United States and Russia out of the Persian Gulf. More and more they warn about a Big Two deal at their expense -- a "second Yalta," as Gen. Zia put it to me in a recent interview.

Some State and Defense Department planners, in these conditions, have felt obliged to take a second look at the security situation in the Gulf. They have accepted the view that the major threat arises from the possibility of subversion promoted by nearby countries linked with the Soviet Union. They have seen that the best way for the United States to inspire confidence is to show a willingness to take risks against those extensions of Soviet influence.

Afghanistan is the most obvious example. Soviet troops are exposed there, and the administration is more and more tilting in the direction of making Moscow pay for the invasion by giving sustained aid to the Afghan resistance.

Libya presents a second case in point. Col. Qaddafi has subsidized subversive moves against Morocco, Egypt and the conservative states of the Arabian peninsula. He has sent troops to Chad, which now menace the regime in the Sudan. But he is not secure against counter-subversion both at home and in Chad.

Ethiopia and South Yemen are both ruled by regimes friendly to Moscow. Both pose threats to countries friendly to the United States -- Somalia and Saudi Arabia, respectively. But both rely heavily on the support of Cuban troops and technicians, so both are vulnerable to pressure on the Cubans to withdraw from the area.

So far, the notion of spoiling the Soviet position is just a gleam in the eyes of the planners. Means have not been worked out or approval received at the highest levels. But to my mind, at least, the application of pressure to the nodes of Soviet interest in the area makes much more sense than trying to build American strong points in what amounts to sand.

If nothing else, the emergence of the spoiler approach shows how far this country is from having solved the central strategic problem of the 1980s. Uncertainty on that score underlies the urgency of settling promptly the squalid fight for primacy between the White House and the State Department.